LMFDB - Embedded newform 21.8.g.b.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,8,Mod(5,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.56008553517$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.16
Character	$\chi$	$=$	21.17
Dual form			21.8.g.b.5.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(17.9825 - 10.3822i) q^{2} +(7.52171 - 46.1565i) q^{3} +(151.580 - 262.545i) q^{4} +(171.660 + 297.324i) q^{5} +(-343.947 - 908.102i) q^{6} +(-505.231 + 753.847i) q^{7} -3637.11i q^{8} +(-2073.85 - 694.352i) q^{9} +(6173.77 + 3564.43i) q^{10} +(963.898 + 556.507i) q^{11} +(-10978.0 - 8971.21i) q^{12} +5040.70i q^{13} +(-1258.73 + 18801.5i) q^{14} +(15014.6 - 5686.86i) q^{15} +(-18358.9 - 31798.6i) q^{16} +(6399.59 - 11084.4i) q^{17} +(-44501.9 + 9044.92i) q^{18} +(24637.3 - 14224.3i) q^{19} +104081. q^{20} +(30994.7 + 28989.9i) q^{21} +23111.1 q^{22} +(-88152.4 + 50894.8i) q^{23} +(-167876. - 27357.3i) q^{24} +(-19872.1 + 34419.4i) q^{25} +(52333.5 + 90644.4i) q^{26} +(-47647.8 + 90498.9i) q^{27} +(121335. + 246914. i) q^{28} -73697.1i q^{29} +(210959. - 258149. i) q^{30} +(157721. + 91060.2i) q^{31} +(-257101. - 148437. i) q^{32} +(32936.6 - 40304.3i) q^{33} -265767. i q^{34} +(-310865. - 20812.0i) q^{35} +(-496653. + 439228. i) q^{36} +(-200519. - 347310. i) q^{37} +(295360. - 511578. i) q^{38} +(232661. + 37914.7i) q^{39} +(1.08140e6 - 624348. i) q^{40} -424658. q^{41} +(858342. + 199518. i) q^{42} -150211. q^{43} +(292216. - 168711. i) q^{44} +(-149550. - 735798. i) q^{45} +(-1.05680e6 + 1.83043e6i) q^{46} +(189300. + 327878. i) q^{47} +(-1.60580e6 + 608204. i) q^{48} +(-313026. - 761733. i) q^{49} +825264. i q^{50} +(-463482. - 378756. i) q^{51} +(1.32341e6 + 764071. i) q^{52} +(-638822. - 368824. i) q^{53} +(82751.8 + 2.12209e6i) q^{54} +382121. i q^{55} +(2.74182e6 + 1.83758e6i) q^{56} +(-471231. - 1.24416e6i) q^{57} +(-765138. - 1.32526e6i) q^{58} +(-540207. + 935666. i) q^{59} +(782870. - 4.80403e6i) q^{60} +(-326231. + 188349. i) q^{61} +3.78162e6 q^{62} +(1.57121e6 - 1.21255e6i) q^{63} -1.46454e6 q^{64} +(-1.49872e6 + 865288. i) q^{65} +(173835. - 1.06673e6i) q^{66} +(1.24603e6 - 2.15819e6i) q^{67} +(-1.94010e6 - 3.36036e6i) q^{68} +(1.68607e6 + 4.45162e6i) q^{69} +(-5.80621e6 + 2.85322e6i) q^{70} +1.89722e6i q^{71} +(-2.52543e6 + 7.54281e6i) q^{72} +(1.63283e6 + 942715. i) q^{73} +(-7.21168e6 - 4.16367e6i) q^{74} +(1.43921e6 + 1.17612e6i) q^{75} -8.62452e6i q^{76} +(-906512. + 445467. i) q^{77} +(4.57747e6 - 1.73373e6i) q^{78} +(2.13852e6 + 3.70403e6i) q^{79} +(6.30300e6 - 1.09171e7i) q^{80} +(3.81872e6 + 2.87996e6i) q^{81} +(-7.63642e6 + 4.40889e6i) q^{82} -3.62840e6 q^{83} +(1.23093e7 - 3.74321e6i) q^{84} +4.39422e6 q^{85} +(-2.70118e6 + 1.55953e6i) q^{86} +(-3.40160e6 - 554328. i) q^{87} +(2.02408e6 - 3.50580e6i) q^{88} +(-2.21547e6 - 3.83731e6i) q^{89} +(-1.03285e7 - 1.16788e7i) q^{90} +(-3.79991e6 - 2.54672e6i) q^{91} +3.08586e7i q^{92} +(5.38935e6 - 6.59492e6i) q^{93} +(6.80819e6 + 3.93071e6i) q^{94} +(8.45849e6 + 4.88351e6i) q^{95} +(-8.78520e6 + 1.07504e7i) q^{96} +3.45013e6i q^{97} +(-1.35375e7 - 1.04480e7i) q^{98} +(-1.61257e6 - 1.82340e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	17.9825	−	10.3822i	1.58944	−	0.917666i	0.596046	−	0.802950i	$-0.296738\pi$
$2$	17.9825	−	10.3822i	1.58944	−	0.917666i	0.993398	−	0.114715i	$-0.0365956\pi$
$3$	7.52171	−	46.1565i	0.160839	−	0.986981i
$3$	7.52171	−	46.1565i	0.160839	−	0.986981i
$4$	151.580	−	262.545i	1.18422	−	2.05113i
$5$	171.660	+	297.324i	0.614151	+	1.06374i	0.990533	+	0.137276i	$0.0438347\pi$
$5$	171.660	+	297.324i	0.614151	+	1.06374i	−0.376382	+	0.926465i	$0.622832\pi$
$6$	−343.947	−	908.102i	−0.650073	−	1.71635i
$7$	−505.231	+	753.847i	−0.556733	+	0.830692i
$7$	−505.231	+	753.847i	−0.556733	+	0.830692i
$8$		−	3637.11i		−	2.51155i
$9$	−2073.85	−	694.352i	−0.948261	−	0.317491i
$10$	6173.77	+	3564.43i	1.95232	+	1.12717i
$11$	963.898	+	556.507i	0.218352	+	0.126065i	0.605187	−	0.796083i	$-0.293098\pi$
$11$	963.898	+	556.507i	0.218352	+	0.126065i	−0.386835	+	0.922149i	$0.626432\pi$
$12$	−10978.0	−	8971.21i	−1.83396	−	1.49871i
$13$			5040.70i			0.636339i	0.948034	+	0.318170i	$0.103068\pi$
$13$			5040.70i			0.636339i	−0.948034	+	0.318170i	$0.896932\pi$
$14$	−1258.73	+	18801.5i	−0.122598	+	1.83123i
$15$	15014.6	−	5686.86i	1.14867	−	0.435064i
$16$	−18358.9	−	31798.6i	−1.12054	−	1.94083i
$17$	6399.59	−	11084.4i	0.315923	−	0.547194i	−0.663711	−	0.747989i	$-0.731019\pi$
$17$	6399.59	−	11084.4i	0.315923	−	0.547194i	0.979633	+	0.200796i	$0.0643527\pi$
$18$	−44501.9	+	9044.92i	−1.79856	+	0.365554i
$19$	24637.3	−	14224.3i	0.824053	−	0.475767i	−0.0277592	−	0.999615i	$-0.508837\pi$
$19$	24637.3	−	14224.3i	0.824053	−	0.475767i	0.851812	+	0.523848i	$0.175504\pi$
$20$	104081.			2.90916
$21$	30994.7	+	28989.9i	0.730332	+	0.683092i
$22$	23111.1			0.462744
$23$	−88152.4	+	50894.8i	−1.51073	+	0.872220i	−0.510808	+	0.859695i	$0.670654\pi$
$23$	−88152.4	+	50894.8i	−1.51073	+	0.872220i	−0.999922	+	0.0125254i	$0.996013\pi$
$24$	−167876.	−	27357.3i	−2.47885	−	0.403956i
$25$	−19872.1	+	34419.4i	−0.254363	+	0.440569i
$26$	52333.5	+	90644.4i	0.583947	+	1.01143i
$27$	−47647.8	+	90498.9i	−0.465875	+	0.884851i
$28$	121335.	+	246914.i	1.04456	+	2.12566i
$29$		−	73697.1i		−	0.561122i	−0.959836	−	0.280561i	$-0.909480\pi$
$29$		−	73697.1i		−	0.561122i	0.959836	−	0.280561i	$-0.0905205\pi$
$30$	210959.	−	258149.i	1.42650	−	1.74561i
$31$	157721.	+	91060.2i	0.950874	+	0.548988i	0.893352	−	0.449357i	$-0.148347\pi$
$31$	157721.	+	91060.2i	0.950874	+	0.548988i	0.0575219	+	0.998344i	$0.481680\pi$
$32$	−257101.	−	148437.i	−1.38701	−	0.800790i
$33$	32936.6	−	40304.3i	0.159544	−	0.195233i
$34$		−	265767.i		−	1.15965i
$35$	−310865.	−	20812.0i	−1.22556	−	0.0820493i
$36$	−496653.	+	439228.i	−1.77417	+	1.56903i
$37$	−200519.	−	347310.i	−0.650804	−	1.12723i	−0.982928	−	0.183990i	$-0.941099\pi$
$37$	−200519.	−	347310.i	−0.650804	−	1.12723i	0.332124	−	0.943236i	$-0.392235\pi$
$38$	295360.	−	511578.i	0.873191	−	1.51241i
$39$	232661.	+	37914.7i	0.628055	+	0.102348i
$40$	1.08140e6	−	624348.i	2.67164	−	1.54247i
$41$	−424658.			−0.962268			−0.481134	−	0.876647i	$-0.659775\pi$
$41$	−424658.			−0.962268			−0.481134	+	0.876647i	$0.659775\pi$
$42$	858342.	+	199518.i	1.78767	+	0.415536i
$43$	−150211.			−0.288113			−0.144057	−	0.989569i	$-0.546015\pi$
$43$	−150211.			−0.288113			−0.144057	+	0.989569i	$0.546015\pi$
$44$	292216.	−	168711.i	0.517154	−	0.298579i
$45$	−149550.	−	735798.i	−0.244648	−	1.20369i
$46$	−1.05680e6	+	1.83043e6i	−1.60081	+	2.77269i
$47$	189300.	+	327878.i	0.265955	+	0.460648i	0.967814	−	0.251668i	$-0.0809792\pi$
$47$	189300.	+	327878.i	0.265955	+	0.460648i	−0.701858	+	0.712317i	$0.747646\pi$
$48$	−1.60580e6	+	608204.i	−2.09579	+	0.793789i
$49$	−313026.	−	761733.i	−0.380097	−	0.924947i
$50$			825264.i			0.933679i
$51$	−463482.	−	378756.i	−0.489257	−	0.399820i
$52$	1.32341e6	+	764071.i	1.30522	+	0.753567i
$53$	−638822.	−	368824.i	−0.589406	−	0.340293i	0.175457	−	0.984487i	$-0.443860\pi$
$53$	−638822.	−	368824.i	−0.589406	−	0.340293i	−0.764862	+	0.644194i	$0.777193\pi$
$54$	82751.8	+	2.12209e6i	0.0715153	+	1.83394i
$55$			382121.i			0.309693i
$56$	2.74182e6	+	1.83758e6i	2.08632	+	1.39826i
$57$	−471231.	−	1.24416e6i	−0.337033	−	0.889846i
$58$	−765138.	−	1.32526e6i	−0.514922	−	0.891872i
$59$	−540207.	+	935666.i	−0.342435	+	0.593115i	−0.984884	−	0.173213i	$-0.944585\pi$
$59$	−540207.	+	935666.i	−0.342435	+	0.593115i	0.642449	+	0.766328i	$0.277918\pi$
$60$	782870.	−	4.80403e6i	0.467908	−	2.87129i
$61$	−326231.	+	188349.i	−0.184022	+	0.106245i	−0.589181	−	0.808001i	$-0.700550\pi$
$61$	−326231.	+	188349.i	−0.184022	+	0.106245i	0.405159	+	0.914246i	$0.367216\pi$
$62$	3.78162e6			2.01515
$63$	1.57121e6	−	1.21255e6i	0.791665	−	0.610955i
$64$	−1.46454e6			−0.698349
$65$	−1.49872e6	+	865288.i	−0.676900	+	0.390808i
$66$	173835.	−	1.06673e6i	0.0744274	−	0.456719i
$67$	1.24603e6	−	2.15819e6i	0.506136	−	0.876653i	−0.493839	−	0.869553i	$-0.664407\pi$
$67$	1.24603e6	−	2.15819e6i	0.506136	−	0.876653i	0.999975	−	0.00709942i	$-0.00225983\pi$
$68$	−1.94010e6	−	3.36036e6i	−0.748245	−	1.29600i
$69$	1.68607e6	+	4.45162e6i	0.617880	+	1.63135i
$70$	−5.80621e6	+	2.85322e6i	−2.02325	+	0.994240i
$71$			1.89722e6i			0.629092i	0.949242	+	0.314546i	$0.101852\pi$
$71$			1.89722e6i			0.629092i	−0.949242	+	0.314546i	$0.898148\pi$
$72$	−2.52543e6	+	7.54281e6i	−0.797393	+	2.38160i
$73$	1.63283e6	+	942715.i	0.491260	+	0.283629i	0.725097	−	0.688647i	$-0.241795\pi$
$73$	1.63283e6	+	942715.i	0.491260	+	0.283629i	−0.233837	+	0.972276i	$0.575128\pi$
$74$	−7.21168e6	−	4.16367e6i	−2.06883	−	1.19444i
$75$	1.43921e6	+	1.17612e6i	0.393921	+	0.321912i
$76$		−	8.62452e6i		−	2.25365i
$77$	−906512.	+	445467.i	−0.226285	+	0.111198i
$78$	4.57747e6	−	1.73373e6i	1.09218	−	0.413667i
$79$	2.13852e6	+	3.70403e6i	0.488000	+	0.845240i	0.999905	−	0.0138018i	$-0.00439340\pi$
$79$	2.13852e6	+	3.70403e6i	0.488000	+	0.845240i	−0.511905	+	0.859042i	$0.671060\pi$
$80$	6.30300e6	−	1.09171e7i	1.37636	−	2.38393i
$81$	3.81872e6	+	2.87996e6i	0.798399	+	0.602128i
$82$	−7.63642e6	+	4.40889e6i	−1.52947	+	0.883040i
$83$	−3.62840e6			−0.696533			−0.348267	−	0.937396i	$-0.613230\pi$
$83$	−3.62840e6			−0.696533			−0.348267	+	0.937396i	$0.613230\pi$
$84$	1.23093e7	−	3.74321e6i	2.26599	−	0.689075i
$85$	4.39422e6			0.776096
$86$	−2.70118e6	+	1.55953e6i	−0.457940	+	0.264392i
$87$	−3.40160e6	−	554328.i	−0.553816	−	0.0902505i
$88$	2.02408e6	−	3.50580e6i	0.316619	−	0.548401i
$89$	−2.21547e6	−	3.83731e6i	−0.333120	−	0.576982i	0.650002	−	0.759933i	$-0.274768\pi$
$89$	−2.21547e6	−	3.83731e6i	−0.333120	−	0.576982i	−0.983122	+	0.182951i	$0.941435\pi$
$90$	−1.03285e7	−	1.16788e7i	−1.49344	−	1.68869i
$91$	−3.79991e6	−	2.54672e6i	−0.528602	−	0.354271i
$92$			3.08586e7i			4.13161i
$93$	5.38935e6	−	6.59492e6i	0.694778	−	0.850196i
$94$	6.80819e6	+	3.93071e6i	0.845443	+	0.488117i
$95$	8.45849e6	+	4.88351e6i	1.01219	+	0.584386i
$96$	−8.78520e6	+	1.07504e7i	−1.01345	+	1.24015i
$97$			3.45013e6i			0.383826i	0.981412	+	0.191913i	$0.0614692\pi$
$97$			3.45013e6i			0.383826i	−0.981412	+	0.191913i	$0.938531\pi$
$98$	−1.35375e7	−	1.04480e7i	−1.45294	−	1.12135i
$99$	−1.61257e6	−	1.82340e6i	−0.167030	−	0.188868i
$100$	6.02443e6	+	1.04346e7i	0.602443	+	1.04346i
$101$	6.74929e6	−	1.16901e7i	0.651828	−	1.12900i	−0.330851	−	0.943683i	$-0.607336\pi$
$101$	6.74929e6	−	1.16901e7i	0.651828	−	1.12900i	0.982679	−	0.185316i	$-0.0593309\pi$
$102$	−1.22669e7	−	1.99902e6i	−1.14455	−	0.186517i
$103$	−2.31712e6	+	1.33779e6i	−0.208938	+	0.120631i	−0.600818	−	0.799386i	$-0.705158\pi$
$103$	−2.31712e6	+	1.33779e6i	−0.208938	+	0.120631i	0.391880	+	0.920017i	$0.371825\pi$
$104$	1.83336e7			1.59820
$105$	−3.29885e6	+	1.41919e7i	−0.278099	+	1.19641i
$106$	−1.53168e7			−1.24910
$107$	7.23780e6	−	4.17874e6i	0.571167	−	0.329764i	−0.186448	−	0.982465i	$-0.559698\pi$
$107$	7.23780e6	−	4.17874e6i	0.571167	−	0.329764i	0.757615	+	0.652701i	$0.226364\pi$
$108$	1.65376e7	+	2.62275e7i	1.26325	+	2.00343i
$109$	1.00892e7	−	1.74751e7i	0.746218	−	1.29249i	−0.203406	−	0.979095i	$-0.565201\pi$
$109$	1.00892e7	−	1.74751e7i	0.746218	−	1.29249i	0.949624	−	0.313393i	$-0.101466\pi$
$110$	3.96726e6	+	6.87149e6i	0.284195	+	0.492239i
$111$	−1.75389e7	+	6.64291e6i	−1.21723	+	0.461029i
$112$	3.32468e7	+	2.22582e6i	2.23608	+	0.149702i
$113$			1.07711e7i			0.702237i	0.936331	+	0.351119i	$0.114199\pi$
$113$			1.07711e7i			0.702237i	−0.936331	+	0.351119i	$0.885801\pi$
$114$	−2.13911e7	−	1.74807e7i	−1.35228	−	1.10508i
$115$	−3.02646e7	−	1.74732e7i	−1.85563	−	1.07135i
$116$	−1.93488e7	−	1.11710e7i	−1.15094	−	0.664493i
$117$	3.50002e6	−	1.04536e7i	0.202032	−	0.603416i
$118$			2.24342e7i			1.25696i
$119$	5.12267e6	+	1.04245e7i	0.278665	+	0.567075i
$120$	−2.06837e7	−	5.46099e7i	−1.09268	−	2.88494i
$121$	−9.12419e6	−	1.58036e7i	−0.468215	−	0.810972i
$122$	−3.91097e6	+	6.77399e6i	−0.194995	+	0.337742i
$123$	−3.19416e6	+	1.96007e7i	−0.154771	+	0.949740i
$124$	4.78148e7	−	2.76059e7i	2.25209	−	1.30025i
$125$	1.31769e7			0.603434
$126$	1.56652e7	−	3.81174e7i	0.697654	−	1.69756i
$127$	4.20872e7			1.82321			0.911606	−	0.411066i	$-0.134843\pi$
$127$	4.20872e7			1.82321			0.911606	+	0.411066i	$0.134843\pi$
$128$	6.57277e6	−	3.79479e6i	0.277022	−	0.159939i
$129$	−1.12985e6	+	6.93324e6i	−0.0463400	+	0.284362i
$130$	−1.79672e7	+	3.11201e7i	−0.717263	+	1.24234i
$131$	−1.06475e7	−	1.84420e7i	−0.413807	−	0.716734i	0.581496	−	0.813550i	$-0.302468\pi$
$131$	−1.06475e7	−	1.84420e7i	−0.413807	−	0.716734i	−0.995302	+	0.0968151i	$0.969134\pi$
$132$	−5.58915e6	−	1.47567e7i	−0.211513	−	0.558444i
$133$	−1.72455e6	+	2.57593e7i	−0.0635615	+	0.949409i
$134$		−	5.17462e7i		−	1.85785i
$135$	−3.50868e7	+	1.36823e6i	−1.22737	+	0.0478619i
$136$	−4.03152e7	−	2.32760e7i	−1.37430	−	0.793455i
$137$	−1.67679e7	−	9.68096e6i	−0.557131	−	0.321659i	0.194862	−	0.980831i	$-0.437574\pi$
$137$	−1.67679e7	−	9.68096e6i	−0.557131	−	0.321659i	−0.751993	+	0.659171i	$0.770907\pi$
$138$	7.65374e7	+	6.25462e7i	2.47912	+	2.02593i
$139$			4.20425e7i			1.32781i	0.747816	+	0.663906i	$0.231103\pi$
$139$			4.20425e7i			1.32781i	−0.747816	+	0.663906i	$0.768897\pi$
$140$	−5.25851e7	+	7.84614e7i	−1.61963	+	2.41662i
$141$	1.65576e7	−	6.27124e6i	0.497427	−	0.188403i
$142$	1.96974e7	+	3.41169e7i	0.577297	+	0.999907i
$143$	−2.80518e6	+	4.85872e6i	−0.0802204	+	0.138946i
$144$	1.59942e7	+	7.86930e7i	0.446369	+	2.19618i
$145$	2.19119e7	−	1.26509e7i	0.596888	−	0.344613i
$146$	3.91498e7			1.04111
$147$	−3.75134e7	+	8.71867e6i	−0.974039	+	0.226381i
$148$	−1.21579e8			−3.08279
$149$	1.18156e7	−	6.82176e6i	0.292621	−	0.168945i	−0.346502	−	0.938049i	$-0.612631\pi$
$149$	1.18156e7	−	6.82176e6i	0.292621	−	0.168945i	0.639123	+	0.769104i	$0.279297\pi$
$150$	3.80913e7	+	6.20740e6i	0.921523	+	0.150172i
$151$	2.60907e7	−	4.51904e7i	0.616688	−	1.06814i	−0.373397	−	0.927672i	$-0.621807\pi$
$151$	2.60907e7	−	4.51904e7i	0.616688	−	1.06814i	0.990086	−	0.140464i	$-0.0448595\pi$
$152$	−5.17355e7	−	8.96085e7i	−1.19491	−	2.06965i
$153$	−2.09682e7	+	1.85438e7i	−0.473306	+	0.418580i
$154$	−1.16764e7	+	1.74222e7i	−0.257625	+	0.384398i
$155$			6.25257e7i			1.34864i
$156$	4.52211e7	−	5.53368e7i	0.953686	−	1.16702i
$157$	3.24662e7	+	1.87444e7i	0.669550	+	0.386565i	0.795906	−	0.605420i	$-0.206995\pi$
$157$	3.24662e7	+	1.87444e7i	0.669550	+	0.386565i	−0.126356	+	0.991985i	$0.540328\pi$
$158$	7.69121e7	+	4.44052e7i	1.55130	+	0.895641i
$159$	−2.18287e7	+	2.67116e7i	−0.430663	+	0.526999i
$160$		−	1.01923e8i		−	1.96722i
$161$	6.17044e6	−	9.21670e7i	0.116527	−	1.74054i
$162$	9.85705e7	+	1.21422e7i	1.82156	+	0.224385i
$163$	−4.72084e7	−	8.17673e7i	−0.853813	−	1.47885i	−0.877742	−	0.479133i	$-0.840951\pi$
$163$	−4.72084e7	−	8.17673e7i	−0.853813	−	1.47885i	0.0239292	−	0.999714i	$-0.492382\pi$
$164$	−6.43698e7	+	1.11492e8i	−1.13954	+	1.97374i
$165$	1.76374e7	+	2.87420e6i	0.305661	+	0.0498108i
$166$	−6.52477e7	+	3.76708e7i	−1.10710	+	0.639185i
$167$	−2.74004e7			−0.455249			−0.227625	−	0.973749i	$-0.573096\pi$
$167$	−2.74004e7			−0.455249			−0.227625	+	0.973749i	$0.573096\pi$
$168$	1.05440e8	−	1.12731e8i	1.71562	−	1.83426i
$169$	3.73399e7			0.595072
$170$	7.90191e7	−	4.56217e7i	1.23356	−	0.712197i
$171$	−6.09706e7	+	1.23922e7i	−0.932469	+	0.189523i
$172$	−2.27691e7	+	3.94373e7i	−0.341190	+	0.590959i
$173$	3.16457e7	+	5.48120e7i	0.464680	+	0.804849i	0.999187	−	0.0403150i	$-0.0128361\pi$
$173$	3.16457e7	+	5.48120e7i	0.464680	+	0.804849i	−0.534507	+	0.845164i	$0.679503\pi$
$174$	−6.69244e7	+	2.53479e7i	−0.963080	+	0.364770i
$175$	−1.59070e7	−	3.23703e7i	−0.224365	−	0.456576i
$176$		−	4.08675e7i		−	0.565046i
$177$	3.91238e7	+	3.19719e7i	0.530316	+	0.433373i
$178$	−7.96795e7	−	4.60030e7i	−1.05895	−	0.611387i
$179$	−1.77639e7	−	1.02560e7i	−0.231501	−	0.133657i	0.379763	−	0.925084i	$-0.376005\pi$
$179$	−1.77639e7	−	1.02560e7i	−0.231501	−	0.133657i	−0.611264	+	0.791426i	$0.709339\pi$
$180$	−2.15849e8	−	7.22691e7i	−2.75865	−	0.923632i
$181$		−	6.65265e6i		−	0.0833911i	−0.999130	−	0.0416956i	$-0.986724\pi$
$181$		−	6.65265e6i		−	0.0833911i	0.999130	−	0.0416956i	$-0.0132760\pi$
$182$	−9.47725e7	−	6.34487e6i	−1.16529	−	0.0780141i
$183$	6.23974e6	+	1.64744e7i	0.0752641	+	0.198715i
$184$	1.85110e8	+	3.20620e8i	2.19062	+	3.79427i
$185$	6.88425e7	−	1.19239e8i	0.799384	−	1.38457i
$186$	2.84443e7	−	1.74546e8i	0.324115	−	1.98891i
$187$	1.23371e7	−	7.12283e6i	0.137965	−	0.0796538i
$188$	1.14777e8			1.25980
$189$	−4.41491e7	−	8.16419e7i	−0.475670	−	0.879624i
$190$	2.02806e8			2.14508
$191$	−1.19679e8	+	6.90967e7i	−1.24280	+	0.717530i	−0.969663	−	0.244445i	$-0.921394\pi$
$191$	−1.19679e8	+	6.90967e7i	−1.24280	+	0.717530i	−0.273136	+	0.961975i	$0.588061\pi$
$192$	−1.10159e7	+	6.75983e7i	−0.112322	+	0.689257i
$193$	−6.84363e7	+	1.18535e8i	−0.685229	+	1.18685i	0.288136	+	0.957590i	$0.406965\pi$
$193$	−6.84363e7	+	1.18535e8i	−0.685229	+	1.18685i	−0.973365	+	0.229262i	$0.926369\pi$
$194$	3.58200e7	+	6.20420e7i	0.352224	+	0.610070i
$195$	2.86657e7	+	7.56843e7i	0.276848	+	0.730945i
$196$	−2.47438e8	−	3.32803e7i	−2.34731	−	0.315712i
$197$		−	9.90561e6i		−	0.0923102i	−0.998934	−	0.0461551i	$-0.985303\pi$
$197$		−	9.90561e6i		−	0.0923102i	0.998934	−	0.0461551i	$-0.0146968\pi$
$198$	−4.79288e7	−	1.60472e7i	−0.438802	−	0.146917i
$199$	2.04011e7	+	1.17786e7i	0.183514	+	0.105952i	0.588943	−	0.808175i	$-0.299544\pi$
$199$	2.04011e7	+	1.17786e7i	0.183514	+	0.105952i	−0.405429	+	0.914127i	$0.632878\pi$
$200$	1.25187e8	+	7.22769e7i	1.10651	+	0.638844i
$201$	−9.02422e7	−	7.37457e7i	−0.783833	−	0.640546i
$202$		−	2.80290e8i		−	2.39264i
$203$	5.55563e7	+	3.72340e7i	0.466119	+	0.312395i
$204$	−1.69695e8	+	6.42728e7i	−1.39947	+	0.530056i
$205$	−7.28970e7	−	1.26261e8i	−0.590978	−	1.02360i
$206$	−2.77784e7	+	4.81136e7i	−0.221397	+	0.383471i
$207$	2.18154e8	−	4.43393e7i	1.70949	−	0.347450i
$208$	1.60287e8	−	9.25418e7i	1.23503	−	0.713044i
$209$	3.16638e7			0.239911
$210$	8.80218e7	+	2.89455e8i	0.655878	+	2.15682i
$211$	−8.68031e6			−0.0636131			−0.0318066	−	0.999494i	$-0.510126\pi$
$211$	−8.68031e6			−0.0636131			−0.0318066	+	0.999494i	$0.510126\pi$
$212$	−1.93666e8	+	1.11813e8i	−1.39597	+	0.805966i
$213$	8.75693e7	+	1.42704e7i	0.620902	+	0.101183i
$214$	8.67692e7	−	1.50289e8i	0.605226	−	1.04828i
$215$	−2.57854e7	−	4.46615e7i	−0.176945	−	0.306478i
$216$	3.29154e8	+	1.73300e8i	2.22234	+	1.17007i
$217$	−1.48331e8	+	7.28909e7i	−0.985422	+	0.484244i
$218$		−	4.18994e8i		−	2.73911i
$219$	5.57941e7	−	6.82749e7i	0.358950	−	0.439245i
$220$	1.00324e8	+	5.79220e7i	0.635221	+	0.366745i
$221$	5.58731e7	+	3.22584e7i	0.348201	+	0.201034i
$222$	−2.46425e8	+	3.01548e8i	−1.51164	+	1.84979i
$223$			1.90665e8i			1.15134i	0.817683	+	0.575669i	$0.195258\pi$
$223$			1.90665e8i			1.15134i	−0.817683	+	0.575669i	$0.804742\pi$
$224$	2.41795e8	−	1.18820e8i	1.43740	−	0.706350i
$225$	6.51109e7	−	5.75825e7i	0.381079	−	0.337017i
$226$	1.11827e8	+	1.93691e8i	0.644419	+	1.11617i
$227$	−1.53279e8	+	2.65487e8i	−0.869747	+	1.50645i	−0.00749097	+	0.999972i	$0.502384\pi$
$227$	−1.53279e8	+	2.65487e8i	−0.869747	+	1.50645i	−0.862256	+	0.506473i	$0.830949\pi$
$228$	−3.98078e8	−	6.48712e7i	−2.22431	−	0.362476i
$229$	2.46718e8	−	1.42443e8i	1.35762	−	0.783820i	0.368313	−	0.929702i	$-0.379935\pi$
$229$	2.46718e8	−	1.42443e8i	1.35762	−	0.783820i	0.989302	+	0.145882i	$0.0466020\pi$
$230$	−7.25643e8			−3.93256
$231$	1.37427e7	+	4.51921e7i	0.0733549	+	0.241224i
$232$	−2.68044e8			−1.40928
$233$	367998.	−	212464.i	0.00190590	−	0.00110037i	−0.499047	−	0.866575i	$-0.666316\pi$
$233$	367998.	−	212464.i	0.00190590	−	0.00110037i	0.500953	+	0.865475i	$0.332983\pi$
$234$	−4.55927e7	−	2.24321e8i	−0.232616	−	1.14449i
$235$	−6.49907e7	+	1.12567e8i	−0.326674	+	0.565815i
$236$	1.63770e8	+	2.83657e8i	0.811038	+	1.40476i
$237$	1.87051e8	−	7.08462e7i	0.912725	−	0.345698i
$238$	2.00348e8	+	1.34274e8i	0.963308	+	0.645613i
$239$			1.59609e8i			0.756250i	0.925755	+	0.378125i	$0.123431\pi$
$239$			1.59609e8i			0.756250i	−0.925755	+	0.378125i	$0.876569\pi$
$240$	−4.56487e8	−	3.73040e8i	−2.13152	−	1.74187i
$241$	6.75215e7	+	3.89835e7i	0.310729	+	0.179400i	0.647253	−	0.762275i	$-0.275918\pi$
$241$	6.75215e7	+	3.89835e7i	0.310729	+	0.179400i	−0.336523	+	0.941675i	$0.609251\pi$
$242$	−3.28151e8	−	1.89458e8i	−1.48840	−	0.859330i
$243$	1.61652e8	−	1.54597e8i	0.722703	−	0.691159i
$244$			1.14200e8i			0.503272i
$245$	1.72748e8	−	2.23830e8i	0.750466	−	0.972381i
$246$	1.46060e8	+	3.85633e8i	0.625545	+	1.65159i
$247$	7.17006e7	+	1.24189e8i	0.302749	+	0.524377i
$248$	3.31196e8	−	5.73648e8i	1.37881	−	2.38817i
$249$	−2.72918e7	+	1.67474e8i	−0.112030	+	0.687465i
$250$	2.36955e8	−	1.36806e8i	0.959124	−	0.553751i
$251$	−1.08662e7			−0.0433730			−0.0216865	−	0.999765i	$-0.506904\pi$
$251$	−1.08662e7			−0.0433730			−0.0216865	+	0.999765i	$0.506904\pi$
$252$	−8.01860e7	−	5.96312e8i	−0.315643	−	2.34732i
$253$	−1.13293e8			−0.439827
$254$	7.56834e8	−	4.36958e8i	2.89789	−	1.67310i
$255$	3.30521e7	−	2.02822e8i	0.124827	−	0.765992i
$256$	1.72527e8	−	2.98826e8i	0.642715	−	1.11321i
$257$	−4.08422e7	−	7.07407e7i	−0.150087	−	0.259958i	0.781172	−	0.624315i	$-0.214622\pi$
$257$	−4.08422e7	−	7.07407e7i	−0.150087	−	0.259958i	−0.931259	+	0.364357i	$0.881289\pi$
$258$	5.16648e7	+	1.36407e8i	0.187295	+	0.494503i
$259$	3.63127e8	+	2.43108e7i	1.29870	+	0.0869461i
$260$			5.24643e8i			1.85122i
$261$	−5.11717e7	+	1.52836e8i	−0.178151	+	0.532090i
$262$	−3.82937e8	−	2.21089e8i	−1.31545	−	0.759473i
$263$	−2.19166e8	−	1.26536e8i	−0.742897	−	0.428912i	0.0802245	−	0.996777i	$-0.474436\pi$
$263$	−2.19166e8	−	1.26536e8i	−0.742897	−	0.428912i	−0.823122	+	0.567865i	$0.807770\pi$
$264$	−1.46591e8	−	1.19794e8i	−0.490336	−	0.400702i
$265$		−	2.53250e8i		−	0.835966i
$266$	2.36427e8	+	4.81121e8i	0.770213	+	1.56736i
$267$	−1.93781e8	+	7.33953e7i	−0.623048	+	0.235982i
$268$	−3.77748e8	−	6.54278e8i	−1.19875	−	2.07630i
$269$	−2.80671e8	+	4.86136e8i	−0.879153	+	1.52274i	−0.0268802	+	0.999639i	$0.508557\pi$
$269$	−2.80671e8	+	4.86136e8i	−0.879153	+	1.52274i	−0.852272	+	0.523098i	$0.824776\pi$
$270$	−6.16743e8	+	3.88882e8i	−1.90691	+	1.20239i
$271$	−4.04205e8	+	2.33368e8i	−1.23370	+	0.712277i	−0.967799	−	0.251724i	$-0.919003\pi$
$271$	−4.04205e8	+	2.33368e8i	−1.23370	+	0.712277i	−0.265900	+	0.964001i	$0.585669\pi$
$272$	−4.69958e8			−1.41602
$273$	−1.46129e8	+	1.56235e8i	−0.434679	+	0.464739i
$274$	−4.02039e8			−1.18070
$275$	−3.83093e7	+	2.21179e7i	−0.111081	+	0.0641327i
$276$	1.42433e9	+	2.32110e8i	4.07782	+	0.664525i
$277$	−6.41350e7	+	1.11085e8i	−0.181307	+	0.314034i	−0.942326	−	0.334696i	$-0.891366\pi$
$277$	−6.41350e7	+	1.11085e8i	−0.181307	+	0.314034i	0.761019	+	0.648730i	$0.224700\pi$
$278$	4.36494e8	+	7.56029e8i	1.21849	+	2.11048i
$279$	−2.63861e8	−	2.98359e8i	−0.727379	−	0.822477i
$280$	−7.56954e7	+	1.13065e9i	−0.206071	+	3.07805i
$281$		−	3.38344e7i		−	0.0909675i	−0.998965	−	0.0454837i	$-0.985517\pi$
$281$		−	3.38344e7i		−	0.0909675i	0.998965	−	0.0454837i	$-0.0144829\pi$
$282$	2.32637e8	−	2.84677e8i	0.617742	−	0.755927i
$283$	−2.30523e8	−	1.33092e8i	−0.604590	−	0.349060i	0.166255	−	0.986083i	$-0.446832\pi$
$283$	−2.30523e8	−	1.33092e8i	−0.604590	−	0.349060i	−0.770845	+	0.637023i	$0.780166\pi$
$284$	4.98107e8	+	2.87582e8i	1.29035	+	0.744985i
$285$	2.89028e8	−	3.53682e8i	0.739576	−	0.905015i
$286$			1.16496e8i			0.294462i
$287$	2.14550e8	−	3.20127e8i	0.535726	−	0.799348i
$288$	4.30121e8	+	4.86355e8i	1.06100	+	1.19972i
$289$	1.23260e8	+	2.13492e8i	0.300386	+	0.520284i
$290$	2.62688e8	−	4.54989e8i	0.632480	−	1.09549i
$291$	1.59246e8	+	2.59509e7i	0.378829	+	0.0617343i
$292$	4.95010e8	−	2.85794e8i	1.16352	−	0.671759i
$293$	3.87975e8			0.901088			0.450544	−	0.892754i	$-0.351230\pi$
$293$	3.87975e8			0.901088			0.450544	+	0.892754i	$0.351230\pi$
$294$	−5.84067e8	+	5.46256e8i	−1.34044	+	1.25366i
$295$	−3.70928e8			−0.841227
$296$	−1.26320e9	+	7.29311e8i	−2.83108	+	1.63453i
$297$	−9.62908e7	+	6.07154e7i	−0.213274	+	0.134478i
$298$	1.41650e8	−	2.45345e8i	0.310070	−	0.537056i
$299$	−2.56545e8	−	4.44350e8i	−0.555028	−	0.961337i
$300$	5.26940e8	−	1.99581e8i	1.12677	−	0.426770i
$301$	7.58915e7	−	1.13236e8i	0.160402	−	0.239333i
$302$		−	1.08351e9i		−	2.26366i
$303$	−4.88808e8	−	3.99453e8i	−1.00946	−	0.824929i
$304$	−9.04628e8	−	5.22287e8i	−1.84677	−	1.06623i
$305$	−1.12002e8	−	6.46643e7i	−0.226035	−	0.130501i
$306$	−1.84536e8	+	5.51161e8i	−0.368177	+	1.09965i
$307$		−	2.45426e8i		−	0.484101i	−0.970264	−	0.242051i	$-0.922180\pi$
$307$		−	2.45426e8i		−	0.484101i	0.970264	−	0.242051i	$-0.0778200\pi$
$308$	−2.04544e7	+	3.05524e8i	−0.0398895	+	0.595824i
$309$	4.43190e7	+	1.17013e8i	0.0854546	+	0.225620i
$310$	6.49155e8	+	1.12437e9i	1.23761	+	2.14360i
$311$	2.53214e8	−	4.38580e8i	0.477339	−	0.826776i	−0.522324	−	0.852747i	$-0.674935\pi$
$311$	2.53214e8	−	4.38580e8i	0.477339	−	0.826776i	0.999663	+	0.0259718i	$0.00826801\pi$
$312$	1.37900e8	−	8.46214e8i	0.257053	−	1.57739i
$313$	−2.84349e8	+	1.64169e8i	−0.524138	+	0.302611i	−0.738626	−	0.674115i	$-0.764525\pi$
$313$	−2.84349e8	+	1.64169e8i	−0.524138	+	0.302611i	0.214488	+	0.976727i	$0.431192\pi$
$314$	7.78432e8			1.41895
$315$	6.30236e8	+	2.59011e8i	1.13610	+	0.466907i
$316$	1.29663e9			2.31160
$317$	−6.25926e8	+	3.61379e8i	−1.10361	+	0.637170i	−0.937167	−	0.348881i	$-0.886562\pi$
$317$	−6.25926e8	+	3.61379e8i	−1.10361	+	0.637170i	−0.166444	+	0.986051i	$0.553228\pi$
$318$	−1.15209e8	+	7.06971e8i	−0.200905	+	1.23284i
$319$	4.10129e7	−	7.10365e7i	0.0707381	−	0.122522i
$320$	−2.51404e8	−	4.35445e8i	−0.428892	−	0.742862i
$321$	−1.38436e8	−	3.65503e8i	−0.233604	−	0.616770i
$322$	−8.45937e8	−	1.72146e9i	−1.41203	−	2.87343i
$323$		−	3.64119e8i		−	0.601222i
$324$	1.33496e9	−	5.66040e8i	2.18053	−	0.924569i
$325$	−1.73498e8	−	1.00169e8i	−0.280351	−	0.161861i
$326$	−1.69785e9	−	9.80255e8i	−2.71418	−	1.56703i
$327$	−7.30700e8	−	5.97126e8i	−1.15564	−	0.944385i
$328$			1.54453e9i			2.41678i
$329$	−3.42810e8	−	2.29506e7i	−0.530723	−	0.0355311i
$330$	3.47005e8	−	1.31429e8i	0.531540	−	0.201323i
$331$	2.19348e8	+	3.79922e8i	0.332457	+	0.575833i	0.982993	−	0.183643i	$-0.0587890\pi$
$331$	2.19348e8	+	3.79922e8i	0.332457	+	0.575833i	−0.650536	+	0.759475i	$0.725456\pi$
$332$	−5.49994e8	+	9.52618e8i	−0.824850	+	1.42868i
$333$	1.74691e8	+	8.59499e8i	0.259249	+	1.27553i
$334$	−4.92728e8	+	2.84477e8i	−0.723594	+	0.417767i
$335$	8.55576e8			1.24337
$336$	3.52809e8	−	1.51781e9i	0.507402	−	2.18289i
$337$	−3.32774e8			−0.473636			−0.236818	−	0.971554i	$-0.576105\pi$
$337$	−3.32774e8			−0.473636			−0.236818	+	0.971554i	$0.576105\pi$
$338$	6.71465e8	−	3.87670e8i	0.945834	−	0.546077i
$339$	4.97155e8	+	8.10168e7i	0.693095	+	0.112947i
$340$	6.66078e8	−	1.15368e9i	0.919070	−	1.59188i
$341$	1.01351e8	+	1.75545e8i	0.138417	+	0.239745i
$342$	−9.67747e8	+	8.55852e8i	−1.30819	+	1.15693i
$343$	7.32381e8	+	1.48877e8i	0.979958	+	0.199205i
$344$			5.46336e8i			0.723611i
$345$	−1.03415e9	+	1.26548e9i	−1.35586	+	1.65916i
$346$	1.13814e9	+	6.57105e8i	1.47716	+	0.852842i
$347$	1.24932e9	+	7.21293e8i	1.60516	+	0.926741i	0.990432	+	0.138005i	$0.0440689\pi$
$347$	1.24932e9	+	7.21293e8i	1.60516	+	0.926741i	0.614731	+	0.788737i	$0.289264\pi$
$348$	−6.61152e8	+	8.09048e8i	−0.840957	+	1.02907i
$349$		−	7.76311e8i		−	0.977568i	−0.872405	−	0.488784i	$-0.837441\pi$
$349$		−	7.76311e8i		−	0.977568i	0.872405	−	0.488784i	$-0.162559\pi$
$350$	−6.22122e8	−	4.16949e8i	−0.775600	−	0.519810i
$351$	−4.56177e8	−	2.40178e8i	−0.563065	−	0.296455i
$352$	−1.65213e8	−	2.86157e8i	−0.201904	−	0.349708i
$353$	−1.18513e7	+	2.05270e7i	−0.0143401	+	0.0248378i	−0.873106	−	0.487530i	$-0.837898\pi$
$353$	−1.18513e7	+	2.05270e7i	−0.0143401	+	0.0248378i	0.858766	+	0.512367i	$0.171231\pi$
$354$	1.03548e9	+	1.68743e8i	1.24060	+	0.202169i
$355$	−5.64091e8	+	3.25678e8i	−0.669191	+	0.386358i
$356$	−1.34329e9			−1.57795
$357$	5.19689e8	−	1.58035e8i	0.604512	−	0.183829i
$358$	−4.25920e8			−0.490611
$359$	8.50226e7	−	4.90878e7i	0.0969848	−	0.0559942i	−0.450723	−	0.892664i	$-0.648834\pi$
$359$	8.50226e7	−	4.90878e7i	0.0969848	−	0.0559942i	0.547708	+	0.836670i	$0.315501\pi$
$360$	−2.67618e9	+	5.43928e8i	−3.02313	+	0.614445i
$361$	−4.22724e7	+	7.32179e7i	−0.0472913	+	0.0819110i
$362$	−6.90692e7	−	1.19631e8i	−0.0765252	−	0.132546i
$363$	−7.98066e8	+	3.02271e8i	−0.875721	+	0.331683i
$364$	−1.24462e9	+	6.11615e8i	−1.35264	+	0.664697i
$365$			6.47307e8i			0.696764i
$366$	2.83247e8	+	2.31469e8i	0.301982	+	0.246779i
$367$	1.47022e9	+	8.48833e8i	1.55257	+	0.896378i	0.997931	+	0.0642877i	$0.0204775\pi$
$367$	1.47022e9	+	8.48833e8i	1.55257	+	0.896378i	0.554640	+	0.832090i	$0.312856\pi$
$368$	3.23677e9	+	1.86875e9i	3.38567	+	1.95472i
$369$	8.80676e8	+	2.94862e8i	0.912481	+	0.305511i
$370$		−	2.85895e9i		−	2.93427i
$371$	6.00789e8	−	2.95232e8i	0.610820	−	0.300162i
$372$	−9.14542e8	−	2.41461e9i	−0.921093	−	2.43190i
$373$	−9.34039e6	−	1.61780e7i	−0.00931932	−	0.0161415i	0.861328	−	0.508049i	$-0.169633\pi$
$373$	−9.34039e6	−	1.61780e7i	−0.00931932	−	0.0161415i	−0.870647	+	0.491908i	$0.836300\pi$
$374$	1.47901e8	−	2.56173e8i	0.146191	−	0.253211i
$375$	9.91132e7	−	6.08202e8i	0.0970559	−	0.595578i
$376$	1.19253e9	−	6.88506e8i	1.15694	−	0.667960i
$377$	3.71485e8			0.357064
$378$	−1.64154e9	−	1.00976e9i	−1.56325	−	0.961606i
$379$	1.03410e9			0.975719			0.487860	−	0.872922i	$-0.337778\pi$
$379$	1.03410e9			0.975719			0.487860	+	0.872922i	$0.337778\pi$
$380$	2.56428e9	−	1.48049e9i	2.39730	−	1.38408i
$381$	3.16568e8	−	1.94260e9i	0.293244	−	1.79947i
$382$	−1.43475e9	+	2.48506e9i	−1.31691	+	2.28095i
$383$	−3.08242e8	−	5.33890e8i	−0.280347	−	0.485575i	0.691123	−	0.722737i	$-0.257116\pi$
$383$	−3.08242e8	−	5.33890e8i	−0.280347	−	0.485575i	−0.971470	+	0.237162i	$0.923783\pi$
$384$	−1.25716e8	−	3.31920e8i	−0.113300	−	0.299139i
$385$	−2.88060e8	−	1.93059e8i	−0.257259	−	0.172416i
$386$			2.84208e9i			2.51525i
$387$	3.11516e8	+	1.04300e8i	0.273207	+	0.0914733i
$388$	9.05814e8	+	5.22972e8i	0.787278	+	0.454535i
$389$	−6.08199e8	−	3.51144e8i	−0.523868	−	0.302455i	0.214648	−	0.976692i	$-0.431140\pi$
$389$	−6.08199e8	−	3.51144e8i	−0.523868	−	0.302455i	−0.738516	+	0.674236i	$0.764473\pi$
$390$	1.30125e9	+	1.06338e9i	1.11080	+	0.907741i
$391$			1.30282e9i			1.10222i
$392$	−2.77051e9	+	1.13851e9i	−2.32305	+	0.954632i
$393$	−9.31305e8	+	3.52736e8i	−0.773959	+	0.293140i
$394$	−1.02842e8	−	1.78128e8i	−0.0847099	−	0.146722i
$395$	−7.34200e8	+	1.27167e9i	−0.599411	+	1.03821i
$396$	−7.23157e8	+	1.46980e8i	−0.585193	+	0.118939i
$397$	5.10835e8	−	2.94931e8i	0.409745	−	0.236566i	−0.280935	−	0.959727i	$-0.590645\pi$
$397$	5.10835e8	−	2.94931e8i	0.409745	−	0.236566i	0.690680	+	0.723160i	$0.257311\pi$
$398$	4.89151e8			0.388913
$399$	1.17599e9	+	2.73353e8i	0.926825	+	0.215436i
$400$	1.45932e9			1.14009
$401$	1.88163e8	−	1.08636e8i	0.145724	−	0.0841336i	−0.425365	−	0.905022i	$-0.639854\pi$
$401$	1.88163e8	−	1.08636e8i	0.145724	−	0.0841336i	0.571089	+	0.820888i	$0.306521\pi$
$402$	−2.38842e9	−	3.89220e8i	−1.83367	−	0.298816i
$403$	−4.59007e8	+	7.95023e8i	−0.349342	+	0.605079i
$404$	−2.04612e9	−	3.54398e9i	−1.54382	−	2.67397i
$405$	−2.00760e8	+	1.62977e9i	−0.150170	+	1.21909i
$406$	1.38561e9	+	9.27647e7i	1.02754	+	0.0687926i
$407$		−	4.46362e8i		−	0.328176i
$408$	−1.37758e9	+	1.68573e9i	−1.00417	+	1.22879i
$409$	−1.59990e9	−	9.23704e8i	−1.15628	−	0.667577i	−0.205868	−	0.978580i	$-0.566002\pi$
$409$	−1.59990e9	−	9.23704e8i	−1.15628	−	0.667577i	−0.950409	+	0.311003i	$0.899335\pi$
$410$	−2.62174e9	−	1.51366e9i	−1.87865	−	1.08464i
$411$	−5.72963e8	+	7.01131e8i	−0.407080	+	0.498142i
$412$			8.11131e8i			0.571414i
$413$	−4.32419e8	−	8.79960e8i	−0.302051	−	0.614664i
$414$	3.46261e9	−	3.06225e9i	2.39829	−	2.12099i
$415$	−6.22853e8	−	1.07881e9i	−0.427777	−	0.740931i
$416$	7.48228e8	−	1.29597e9i	0.509574	−	0.882608i
$417$	1.94053e9	+	3.16231e8i	1.31052	+	0.213564i
$418$	5.69394e8	−	3.28740e8i	0.381325	−	0.220158i
$419$	2.39246e9			1.58890			0.794448	−	0.607333i	$-0.207760\pi$
$419$	2.39246e9			1.58890			0.794448	+	0.607333i	$0.207760\pi$
$420$	3.22597e9	+	3.01731e9i	2.12465	+	1.98723i
$421$	−2.88856e9			−1.88666			−0.943331	−	0.331853i	$-0.892326\pi$
$421$	−2.88856e9			−1.88666			−0.943331	+	0.331853i	$0.892326\pi$
$422$	−1.56094e8	+	9.01208e7i	−0.101110	+	0.0583756i
$423$	−1.64917e8	−	8.11410e8i	−0.105944	−	0.521253i
$424$	−1.34145e9	+	2.32347e9i	−0.854663	+	1.48032i
$425$	2.54346e8	+	4.40540e8i	0.160718	+	0.278371i
$426$	1.72287e9	−	6.52545e8i	1.07974	−	0.408956i
$427$	2.28353e7	−	3.41088e8i	0.0141942	−	0.212016i
$428$		−	2.53366e9i		−	1.56205i
$429$	2.03162e8	+	1.66023e8i	0.124234	+	0.101524i
$430$	−9.27371e8	−	5.35418e8i	−0.562489	−	0.324753i
$431$	−2.41459e9	−	1.39407e9i	−1.45269	−	0.838712i	−0.454059	−	0.890972i	$-0.650024\pi$
$431$	−2.41459e9	−	1.39407e9i	−1.45269	−	0.838712i	−0.998634	+	0.0522593i	$0.983358\pi$
$432$	3.75250e9	−	1.46331e8i	2.23938	−	0.0873257i
$433$		−	2.17509e9i		−	1.28757i	−0.765207	−	0.643784i	$-0.777363\pi$
$433$		−	2.17509e9i		−	1.28757i	0.765207	−	0.643784i	$-0.222637\pi$
$434$	−1.91059e9	+	2.85076e9i	−1.12190	+	1.67397i
$435$	−4.19105e8	−	1.10654e9i	−0.244124	−	0.644544i
$436$	−3.05866e9	−	5.29776e9i	−1.76737	−	3.06118i
$437$	−1.44789e9	+	2.50782e9i	−0.829947	+	1.43751i
$438$	2.94474e8	−	1.80702e9i	0.167451	−	1.02755i
$439$	2.88426e9	−	1.66523e9i	1.62708	−	0.939395i	0.642122	−	0.766603i	$-0.278054\pi$
$439$	2.88426e9	−	1.66523e9i	1.62708	−	0.939395i	0.984958	−	0.172792i	$-0.0552789\pi$
$440$	1.38982e9			0.777808
$441$	1.20258e8	+	1.79707e9i	0.0667696	+	0.997768i
$442$	1.33965e9			0.737928
$443$	4.93316e8	−	2.84816e8i	0.269595	−	0.155651i	−0.359108	−	0.933296i	$-0.616919\pi$
$443$	4.93316e8	−	2.84816e8i	0.269595	−	0.155651i	0.628704	+	0.777645i	$0.283586\pi$
$444$	−9.14484e8	+	5.61167e9i	−0.495833	+	3.04265i
$445$	7.60618e8	−	1.31743e9i	0.409172	−	0.708707i
$446$	1.97952e9	+	3.42863e9i	1.05654	+	1.82999i
$447$	−2.25995e8	−	5.96680e8i	−0.119680	−	0.315984i
$448$	7.39933e8	−	1.10404e9i	0.388794	−	0.580113i
$449$			3.83593e7i			0.0199990i	0.999950	+	0.00999950i	$0.00318299\pi$
$449$			3.83593e7i			0.0199990i	−0.999950	+	0.00999950i	$0.996817\pi$
$450$	5.73023e8	−	1.71147e9i	0.296434	−	0.885372i
$451$	−4.09327e8	−	2.36325e8i	−0.210113	−	0.121309i
$452$	2.82789e9	+	1.63268e9i	1.44038	+	0.831605i
$453$	−1.88958e9	−	1.54416e9i	−0.955041	−	0.780458i
$454$			6.36550e9i			3.19255i
$455$	1.04907e8	−	1.56698e9i	0.0522112	−	0.779871i
$456$	−4.52515e9	+	1.71392e9i	−2.23489	+	0.846474i
$457$	1.67785e8	+	2.90611e8i	0.0822329	+	0.142431i	0.904209	−	0.427091i	$-0.140462\pi$
$457$	1.67785e8	+	2.90611e8i	0.0822329	+	0.142431i	−0.821976	+	0.569522i	$0.807128\pi$
$458$	2.95774e9	−	5.12295e9i	1.43857	−	2.49167i
$459$	6.98200e8	+	1.10730e9i	0.337005	+	0.534468i
$460$	−9.17502e9	+	5.29720e9i	−4.39496	+	2.53743i
$461$	−1.91384e9			−0.909815			−0.454907	−	0.890539i	$-0.650328\pi$
$461$	−1.91384e9			−0.909815			−0.454907	+	0.890539i	$0.650328\pi$
$462$	7.16321e8	+	6.69988e8i	0.337957	+	0.316097i
$463$	2.37251e9			1.11090			0.555450	−	0.831550i	$-0.312546\pi$
$463$	2.37251e9			1.11090			0.555450	+	0.831550i	$0.312546\pi$
$464$	−2.34346e9	+	1.35300e9i	−1.08904	+	0.628760i
$465$	2.88597e9	+	4.70300e8i	1.33109	+	0.216915i
$466$	4.41168e6	−	7.64126e6i	0.00201955	−	0.00349796i
$467$	−8.43852e8	−	1.46159e9i	−0.383404	−	0.664076i	0.608142	−	0.793828i	$-0.291915\pi$
$467$	−8.43852e8	−	1.46159e9i	−0.383404	−	0.664076i	−0.991546	+	0.129752i	$0.958582\pi$
$468$	−2.21402e9	−	2.50348e9i	−0.998436	−	1.12897i
$469$	9.97410e8	+	2.02970e9i	0.446446	+	0.908504i
$470$			2.69899e9i			1.19911i
$471$	1.10938e9	−	1.35754e9i	0.489222	−	0.598658i
$472$	3.40312e9	+	1.96479e9i	1.48964	+	0.860042i
$473$	−1.44789e8	−	8.35937e7i	−0.0629101	−	0.0363212i
$474$	2.62810e9	−	3.21599e9i	1.13349	−	1.38704i
$475$			1.13067e9i			0.484069i
$476$	3.51339e9	+	2.35216e8i	1.49315	+	0.0999639i
$477$	1.06873e9	+	1.20845e9i	0.450871	+	0.509818i
$478$	1.65710e9	+	2.87017e9i	0.693985	+	1.20202i
$479$	−1.27726e9	+	2.21228e9i	−0.531012	+	0.919740i	0.468333	+	0.883552i	$0.344855\pi$
$479$	−1.27726e9	+	2.21228e9i	−0.531012	+	0.919740i	−0.999345	+	0.0361879i	$0.988479\pi$
$480$	−4.70442e9	−	7.66638e8i	−1.94161	−	0.316407i
$481$	1.75068e9	−	1.01076e9i	0.717298	−	0.414132i
$482$	1.61894e9			0.658516
$483$	−4.20770e9	−	9.78060e8i	−1.69914	−	0.394958i
$484$	−5.53219e9			−2.21788
$485$	−1.02581e9	+	5.92251e8i	−0.408291	+	0.235727i
$486$	1.30186e9	−	4.45834e9i	0.514443	−	1.76176i
$487$	−1.39113e9	+	2.40951e9i	−0.545778	+	0.945316i	0.452779	+	0.891623i	$0.350433\pi$
$487$	−1.39113e9	+	2.40951e9i	−0.545778	+	0.945316i	−0.998557	+	0.0536932i	$0.982901\pi$
$488$	6.85048e8	+	1.18654e9i	0.266840	+	0.462181i
$489$	−4.12918e9	+	1.56394e9i	−1.59692	+	0.604840i
$490$	7.82590e8	−	5.81852e9i	0.300503	−	2.23422i
$491$			4.40912e9i			1.68100i	0.541815	+	0.840498i	$0.317737\pi$
$491$			4.40912e9i			1.68100i	−0.541815	+	0.840498i	$0.682263\pi$
$492$	4.66190e9	+	3.80970e9i	1.76476	+	1.44216i
$493$	−8.16888e8	−	4.71631e8i	−0.307043	−	0.177271i
$494$	2.57871e9	+	1.48882e9i	0.962406	+	0.555646i
$495$	2.65326e8	−	7.92460e8i	0.0983246	−	0.293670i
$496$		−	6.68707e9i		−	2.46065i
$497$	−1.43022e9	−	9.58537e8i	−0.522582	−	0.350236i
$498$	1.24798e9	+	3.29496e9i	0.452798	+	1.19549i
$499$	−4.38321e8	−	7.59194e8i	−0.157921	−	0.273527i	0.776198	−	0.630490i	$-0.217146\pi$
$499$	−4.38321e8	−	7.59194e8i	−0.157921	−	0.273527i	−0.934119	+	0.356962i	$0.883813\pi$
$500$	1.99737e9	−	3.45954e9i	0.714600	−	1.23772i
$501$	−2.06098e8	+	1.26471e9i	−0.0732220	+	0.449322i
$502$	−1.95402e8	+	1.12815e8i	−0.0689390	+	0.0398020i
$503$	−2.66652e9			−0.934235			−0.467118	−	0.884195i	$-0.654708\pi$
$503$	−2.66652e9			−0.934235			−0.467118	+	0.884195i	$0.654708\pi$
$504$	−4.41020e9	−	5.71465e9i	−1.53444	−	1.98830i
$505$	4.63434e9			1.60128
$506$	−2.03730e9	+	1.17623e9i	−0.699081	+	0.403615i
$507$	2.80860e8	−	1.72348e9i	0.0957110	−	0.587325i
$508$	6.37959e9	−	1.10498e10i	2.15909	−	3.73965i
$509$	2.64744e9	+	4.58549e9i	0.889843	+	1.54125i	0.840060	+	0.542493i	$0.182520\pi$
$509$	2.64744e9	+	4.58549e9i	0.889843	+	1.54125i	0.0497826	+	0.998760i	$0.484147\pi$
$510$	−1.51138e9	−	3.99040e9i	−0.504520	−	1.33205i
$511$	−1.53562e9	+	7.54615e8i	−0.509108	+	0.250180i
$512$		−	6.19340e9i		−	2.03931i
$513$	1.13376e8	+	2.90740e9i	0.0370774	+	0.950812i
$514$	−1.46889e9	−	8.48063e8i	−0.477110	−	0.275459i
$515$	−7.95515e8	−	4.59291e8i	−0.256639	−	0.148171i
$516$	1.64902e9	+	1.34758e9i	0.528388	+	0.431797i
$517$			4.21388e8i			0.134111i
$518$	6.78233e9	−	3.33289e9i	2.14400	−	1.05358i
$519$	2.76796e9	−	1.04838e9i	0.869109	−	0.329179i
$520$	3.14715e9	+	5.45102e9i	0.981534	+	1.70007i
$521$	2.05460e9	−	3.55866e9i	0.636494	−	1.10244i	−0.349702	−	0.936861i	$-0.613717\pi$
$521$	2.05460e9	−	3.55866e9i	0.636494	−	1.10244i	0.986196	−	0.165579i	$-0.0529494\pi$
$522$	6.66584e8	+	3.27966e9i	0.205120	+	1.00921i
$523$	−4.33945e9	+	2.50538e9i	−1.32641	+	0.765805i	−0.984743	−	0.174015i	$-0.944326\pi$
$523$	−4.33945e9	+	2.50538e9i	−1.32641	+	0.765805i	−0.341670	+	0.939820i	$0.610993\pi$
$524$	−6.45580e9			−1.96016
$525$	−1.61375e9	+	4.90731e8i	−0.486718	+	0.148008i
$526$	−5.25488e9			−1.57439
$527$	2.01870e9	−	1.16549e9i	0.600805	−	0.346875i
$528$	−1.88630e9	−	3.07393e8i	−0.557689	−	0.0908816i
$529$	3.47815e9	−	6.02434e9i	1.02154	−	1.76935i
$530$	−2.62929e9	−	4.55407e9i	−0.767138	−	1.32872i
$531$	1.76999e9	−	1.56533e9i	0.513026	−	0.453708i
$532$	6.50157e9	+	4.35738e9i	1.87209	+	1.25468i
$533$		−	2.14057e9i		−	0.612329i
$534$	−2.72266e9	+	3.33171e9i	−0.773748	+	0.946831i
$535$	2.48489e9	+	1.43465e9i	0.701566	+	0.405049i
$536$	−7.84957e9	−	4.53195e9i	−2.20176	−	1.27118i
$537$	−6.06996e8	+	7.42778e8i	−0.169152	+	0.206990i
$538$			1.16559e10i			3.22707i
$539$	1.22184e8	−	9.08435e8i	0.0336089	−	0.249881i
$540$	−4.95924e9	+	9.41925e9i	−1.35531	+	2.57417i
$541$	−2.34109e9	−	4.05489e9i	−0.635665	−	1.10100i	−0.986374	−	0.164520i	$-0.947393\pi$
$541$	−2.34109e9	−	4.05489e9i	−0.635665	−	1.10100i	0.350708	−	0.936485i	$-0.385941\pi$
$542$	−4.84575e9	+	8.39308e9i	−1.30726	+	2.26425i
$543$	−3.07063e8	−	5.00393e7i	−0.0823054	−	0.0134126i
$544$	−3.29068e9	+	1.89988e9i	−0.876375	+	0.505975i
$545$	6.92769e9			1.83316
$546$	−1.00571e9	+	4.32664e9i	−0.264422	+	1.13757i
$547$	1.79128e9			0.467958			0.233979	−	0.972242i	$-0.424825\pi$
$547$	1.79128e9			0.467958			0.233979	+	0.972242i	$0.424825\pi$
$548$	−5.08337e9	+	2.93489e9i	−1.31953	+	0.761832i
$549$	8.07334e8	−	1.64089e8i	0.208233	−	0.0423230i
$550$	−4.59265e8	+	7.95470e8i	−0.117705	+	0.203871i
$551$	−1.04829e9	−	1.81569e9i	−0.266963	−	0.462394i
$552$	1.61910e10	−	6.13242e9i	4.09721	−	1.55183i
$553$	−3.87272e9	−	2.59273e8i	−0.973819	−	0.0651957i
$554$			2.66345e9i			0.665519i
$555$	−4.98583e9	−	4.07441e9i	−1.23797	−	1.01167i
$556$	1.10380e10	+	6.37282e9i	2.72352	+	1.57242i
$557$	−2.22189e9	−	1.28281e9i	−0.544790	−	0.314535i	0.202228	−	0.979338i	$-0.435182\pi$
$557$	−2.22189e9	−	1.28281e9i	−0.544790	−	0.314535i	−0.747018	+	0.664804i	$0.768515\pi$
$558$	−7.84251e9	−	2.62578e9i	−1.91089	−	0.639791i
$559$		−	7.57170e8i		−	0.183338i
$560$	5.04536e9	+	1.02672e10i	1.21404	+	2.47054i
$561$	−2.35969e8	−	6.23013e8i	−0.0564267	−	0.148980i
$562$	−3.51276e8	−	6.08427e8i	−0.0834778	−	0.144588i
$563$	−3.05993e9	+	5.29996e9i	−0.722658	+	1.25168i	0.237273	+	0.971443i	$0.423746\pi$
$563$	−3.05993e9	+	5.29996e9i	−0.722658	+	1.25168i	−0.959931	+	0.280237i	$0.909587\pi$
$564$	8.63319e8	−	5.29770e9i	0.202626	−	1.24340i
$565$	−3.20250e9	+	1.84896e9i	−0.746998	+	0.431280i
$566$	−5.52716e9			−1.28128
$567$	−4.10038e9	+	1.42368e9i	−0.944678	+	0.327999i
$568$	6.90041e9			1.58000
$569$	6.63609e9	−	3.83135e9i	1.51015	−	0.871883i	0.510216	−	0.860046i	$-0.329565\pi$
$569$	6.63609e9	−	3.83135e9i	1.51015	−	0.871883i	0.999930	−	0.0118373i	$-0.00376803\pi$
$570$	1.52545e9	−	9.36084e9i	0.345014	−	2.11716i
$571$	−1.10442e9	+	1.91291e9i	−0.248260	+	0.429999i	−0.963043	−	0.269347i	$-0.913192\pi$
$571$	−1.10442e9	+	1.91291e9i	−0.248260	+	0.429999i	0.714783	+	0.699346i	$0.246525\pi$
$572$	8.50421e8	+	1.47297e9i	0.189998	+	0.329085i
$573$	2.28907e9	+	6.04369e9i	0.508297	+	1.34203i
$574$	5.34530e8	−	7.98419e9i	0.117972	−	1.76214i
$575$		−	4.04554e9i		−	0.887440i
$576$	3.03724e9	+	1.01691e9i	0.662217	+	0.221719i
$577$	−7.63889e9	−	4.41032e9i	−1.65545	−	0.955772i	−0.974777	−	0.223180i	$-0.928356\pi$
$577$	−7.63889e9	−	4.41032e9i	−1.65545	−	0.955772i	−0.680668	−	0.732592i	$-0.738311\pi$
$578$	4.43305e9	+	2.55942e9i	0.954893	+	0.551308i
$579$	4.95641e9	+	4.05037e9i	1.06119	+	0.867200i
$580$		−	7.67049e9i		−	1.63240i
$581$	1.83318e9	−	2.73526e9i	0.387783	−	0.578604i
$582$	3.13307e9	−	1.18666e9i	0.658779	−	0.249515i
$583$	−4.10506e8	−	7.11017e8i	−0.0857985	−	0.148607i
$584$	3.42876e9	−	5.93878e9i	0.712347	−	1.23382i
$585$	3.70894e9	−	7.53834e8i	0.765956	−	0.155679i
$586$	6.97677e9	−	4.02804e9i	1.43223	−	0.826898i
$587$	2.02419e9			0.413064			0.206532	−	0.978440i	$-0.433782\pi$
$587$	2.02419e9			0.413064			0.206532	+	0.978440i	$0.433782\pi$
$588$	−3.39726e9	+	1.11705e10i	−0.689141	+	2.26597i
$589$	5.18108e9			1.04476
$590$	−6.67022e9	+	3.85106e9i	−1.33708	+	0.771965i
$591$	−4.57209e8	−	7.45072e7i	−0.0911083	−	0.0148471i
$592$	−7.36264e9	+	1.27525e10i	−1.45850	+	2.52620i
$593$	3.08824e9	+	5.34898e9i	0.608162	+	1.05337i	0.991543	+	0.129777i	$0.0414262\pi$
$593$	3.08824e9	+	5.34898e9i	0.608162	+	1.05337i	−0.383381	+	0.923590i	$0.625240\pi$
$594$	−1.10119e9	+	2.09153e9i	−0.215581	+	0.409459i
$595$	−2.22010e9	+	3.31257e9i	−0.432078	+	0.644697i
$596$		−	4.13618e9i		−	0.800272i
$597$	6.97111e8	−	8.53050e8i	0.134089	−	0.164083i
$598$	−9.22666e9	−	5.32701e9i	−1.76437	−	1.01866i
$599$	−1.67198e9	−	9.65317e8i	−0.317861	−	0.183517i	0.332578	−	0.943076i	$-0.392082\pi$
$599$	−1.67198e9	−	9.65317e8i	−0.317861	−	0.183517i	−0.650439	+	0.759559i	$0.725415\pi$
$600$	4.27767e9	−	5.23456e9i	0.808497	−	0.989352i
$601$			2.31165e9i			0.434371i	0.976130	+	0.217186i	$0.0696877\pi$
$601$			2.31165e9i			0.434371i	−0.976130	+	0.217186i	$0.930312\pi$
$602$	1.89076e8	−	2.82420e9i	0.0353222	−	0.527603i
$603$	−4.08262e9	+	3.61057e9i	−0.758278	+	0.670603i
$604$	−7.90967e9	−	1.36999e10i	−1.46059	−	2.52982i
$605$	3.13252e9	−	5.42569e9i	0.575109	−	0.996118i
$606$	−1.29372e10	−	2.10826e9i	−2.36149	−	0.384831i
$607$	−1.27385e9	+	7.35455e8i	−0.231183	+	0.133474i	−0.611118	−	0.791540i	$-0.709280\pi$
$607$	−1.27385e9	+	7.35455e8i	−0.231183	+	0.133474i	0.379935	+	0.925013i	$0.375946\pi$
$608$	−8.44570e9			−1.52396
$609$	2.13647e9	−	2.28422e9i	0.383298	−	0.409805i
$610$	−2.68543e9			−0.479027
$611$	−1.65273e9	+	9.54206e8i	−0.293129	+	0.169238i
$612$	1.69021e9	+	8.31598e9i	0.298064	+	1.46651i
$613$	−3.26279e9	+	5.65132e9i	−0.572108	+	0.990919i	0.424242	+	0.905549i	$0.360541\pi$
$613$	−3.26279e9	+	5.65132e9i	−0.572108	+	0.990919i	−0.996349	+	0.0853703i	$0.972793\pi$
$614$	−2.54806e9	−	4.41337e9i	−0.444243	−	0.769452i
$615$	−6.37609e9	+	2.41497e9i	−1.10533	+	0.418648i
$616$	1.62021e9	+	3.29708e9i	0.279280	+	0.568326i
$617$			2.15423e8i			0.0369228i	0.999830	+	0.0184614i	$0.00587678\pi$
$617$			2.15423e8i			0.0369228i	−0.999830	+	0.0184614i	$0.994123\pi$
$618$	2.01182e9	+	1.64405e9i	0.342869	+	0.280192i
$619$	7.72153e9	+	4.45803e9i	1.30854	+	0.755484i	0.981852	−	0.189649i	$-0.0607351\pi$
$619$	7.72153e9	+	4.45803e9i	1.30854	+	0.755484i	0.326685	+	0.945133i	$0.394068\pi$
$620$	1.64158e10	+	9.47767e9i	2.76625	+	1.59709i
$621$	−4.05659e8	−	1.04027e10i	−0.0679737	−	1.74312i
$622$		−	1.05157e10i		−	1.75215i
$623$	4.01207e9	+	2.68602e8i	0.664753	+	0.0445042i
$624$	−3.06577e9	−	8.09437e9i	−0.505119	−	1.33363i
$625$	3.81446e9	+	6.60685e9i	0.624962	+	1.08247i
$626$	−3.40887e9	+	5.90433e9i	−0.555392	+	0.961968i
$627$	2.38166e8	−	1.46149e9i	0.0385872	−	0.236788i
$628$	9.84248e9	−	5.68256e9i	1.58579	−	0.915556i
$629$	−5.13296e9			−0.822415
$630$	1.40223e10	−	1.88558e9i	2.23423	−	0.300437i
$631$	2.86880e9			0.454567			0.227284	−	0.973829i	$-0.427016\pi$
$631$	2.86880e9			0.454567			0.227284	+	0.973829i	$0.427016\pi$
$632$	1.34720e10	−	7.77805e9i	2.12286	−	1.22563i
$633$	−6.52908e7	+	4.00653e8i	−0.0102315	+	0.0627849i
$634$	−7.50382e9	+	1.29970e10i	−1.16942	+	2.02549i
$635$	7.22471e9	+	1.25136e10i	1.11973	+	1.93942i
$636$	3.70420e9	+	9.77996e9i	0.570945	+	1.50743i
$637$	3.83967e9	−	1.57787e9i	0.588580	−	0.241871i
$638$		−	1.70322e9i		−	0.259656i
$639$	1.31734e9	−	3.93455e9i	0.199731	−	0.596544i
$640$	2.25657e9	+	1.30283e9i	0.340266	+	0.196453i
$641$	−6.53951e9	−	3.77559e9i	−0.980713	−	0.566215i	−0.0782275	−	0.996936i	$-0.524926\pi$
$641$	−6.53951e9	−	3.77559e9i	−0.980713	−	0.566215i	−0.902485	+	0.430721i	$0.858259\pi$
$642$	−6.28415e9	−	5.13539e9i	−0.937289	−	0.765951i
$643$		−	1.35180e7i		−	0.00200528i	−0.999999	−	0.00100264i	$-0.999681\pi$
$643$		−	1.35180e7i		−	0.00200528i	0.999999	−	0.00100264i	$-0.000319150\pi$
$644$	−2.32627e10	−	1.55907e10i	−3.43209	−	2.30020i
$645$	−2.25537e9	+	8.54231e8i	−0.330947	+	0.125348i
$646$	−3.78036e9	−	6.54778e9i	−0.551721	−	0.955609i
$647$	8.29222e7	−	1.43625e8i	0.0120367	−	0.0208481i	−0.859944	−	0.510388i	$-0.829502\pi$
$647$	8.29222e7	−	1.43625e8i	0.0120367	−	0.0208481i	0.871981	+	0.489540i	$0.162835\pi$
$648$	1.04747e10	−	1.38891e10i	1.51227	−	2.00522i
$649$	−1.04141e9	+	6.01258e8i	−0.149543	+	0.0863384i
$650$	−4.15990e9			−0.594137
$651$	2.24869e9	+	7.39470e9i	0.319445	+	1.05048i
$652$	−2.86235e10			−4.04441
$653$	8.34102e9	−	4.81569e9i	1.17226	−	0.676803i	0.218046	−	0.975938i	$-0.430032\pi$
$653$	8.34102e9	−	4.81569e9i	1.17226	−	0.676803i	0.954211	+	0.299135i	$0.0966983\pi$
$654$	−1.93393e10	−	3.15155e9i	−2.70345	−	0.440557i
$655$	3.65550e9	−	6.33152e9i	0.508280	−	0.880366i
$656$	7.79627e9	+	1.35035e10i	1.07826	+	1.86760i
$657$	−2.73167e9	−	3.08881e9i	−0.375793	−	0.424925i
$658$	−6.40286e9	+	3.14641e9i	−0.876160	+	0.430552i
$659$			5.54548e9i			0.754814i	0.926048	+	0.377407i	$0.123184\pi$
$659$			5.54548e9i			0.754814i	−0.926048	+	0.377407i	$0.876816\pi$
$660$	3.42808e9	−	4.19493e9i	0.464139	−	0.567964i
$661$	1.55339e9	+	8.96849e8i	0.209206	+	0.120785i	0.600943	−	0.799292i	$-0.294792\pi$
$661$	1.55339e9	+	8.96849e8i	0.209206	+	0.120785i	−0.391736	+	0.920078i	$0.628125\pi$
$662$	7.88885e9	+	4.55463e9i	1.05684	+	0.610169i
$663$	1.90920e9	−	2.33627e9i	0.254421	−	0.311334i
$664$			1.31969e10i			1.74938i
$665$	−7.95491e9	+	3.90910e9i	−1.04896	+	0.515467i
$666$	1.20649e10	+	1.36423e10i	1.58257	+	1.78948i
$667$	3.75080e9	+	6.49657e9i	0.489422	+	0.847704i
$668$	−4.15336e9	+	7.19384e9i	−0.539116	+	0.933777i
$669$	8.80041e9	+	1.43412e9i	1.13635	+	0.185180i
$670$	1.53854e10	−	8.88277e9i	1.97627	−	1.14100i
$671$	−4.19271e8			−0.0535755
$672$	−3.66559e9	−	1.20541e10i	−0.465963	−	1.53230i
$673$	−9.01100e9			−1.13952			−0.569758	−	0.821813i	$-0.692963\pi$
$673$	−9.01100e9			−1.13952			−0.569758	+	0.821813i	$0.692963\pi$
$674$	−5.98412e9	+	3.45493e9i	−0.752819	+	0.434640i
$675$	−2.16806e9	−	3.43841e9i	−0.271336	−	0.430323i
$676$	5.66000e9	−	9.80340e9i	0.704697	−	1.22057i
$677$	−2.58984e9	−	4.48573e9i	−0.320784	−	0.555614i	0.659866	−	0.751383i	$-0.270613\pi$
$677$	−2.58984e9	−	4.48573e9i	−0.320784	−	0.555614i	−0.980650	+	0.195769i	$0.937280\pi$
$678$	9.78122e9	−	3.70468e9i	1.20528	−	0.456506i
$679$	−2.60087e9	−	1.74311e9i	−0.318841	−	0.213689i
$680$		−	1.59823e10i		−	1.94920i
$681$	1.11010e10	+	9.07175e9i	1.34694	+	1.10072i
$682$	3.64510e9	+	2.10450e9i	0.440011	+	0.254041i
$683$	−3.78775e9	−	2.18686e9i	−0.454893	−	0.262633i	0.255001	−	0.966941i	$-0.417924\pi$
$683$	−3.78775e9	−	2.18686e9i	−0.454893	−	0.262633i	−0.709894	+	0.704308i	$0.751257\pi$
$684$	−5.98845e9	+	1.78859e10i	−0.715514	+	2.13705i
$685$		−	6.64735e9i		−	0.790190i
$686$	1.47157e10	−	4.92654e9i	1.74039	−	0.582649i
$687$	−4.71892e9	−	1.24591e10i	−0.555257	−	1.46601i
$688$	2.75772e9	+	4.77652e9i	0.322843	+	0.559180i
$689$	1.85913e9	−	3.22011e9i	0.216542	−	0.375062i
$690$	−5.45808e9	+	3.34932e10i	−0.632511	+	3.88136i
$691$	−4.05704e9	+	2.34234e9i	−0.467774	+	0.270070i	−0.715308	−	0.698810i	$-0.753713\pi$
$691$	−4.05704e9	+	2.34234e9i	−0.467774	+	0.270070i	0.247533	+	0.968879i	$0.420380\pi$
$692$	1.91875e10			2.20114
$693$	2.18928e9	−	2.94392e8i	0.249882	−	0.0336016i
$694$	2.99544e10			3.40176
$695$	−1.25003e10	+	7.21703e9i	−1.41245	+	0.815477i
$696$	−2.01615e9	+	1.23720e10i	−0.226668	+	1.39094i
$697$	−2.71764e9	+	4.70708e9i	−0.304002	+	0.526547i
$698$	−8.05982e9	−	1.39600e10i	−0.897081	−	1.55379i
$699$	−7.03861e6	−	1.85836e7i	−0.000779501	−	0.00205807i
$700$	−1.09098e10	−	7.30397e8i	−1.20220	−	0.0804851i
$701$			5.56974e8i			0.0610692i	0.999534	+	0.0305346i	$0.00972098\pi$
$701$			5.56974e8i			0.0610692i	−0.999534	+	0.0305346i	$0.990279\pi$
$702$	−1.06968e10	+	4.17127e8i	−1.16701	+	0.0455080i
$703$	−9.88050e9	−	5.70451e9i	−1.07259	−	0.619262i
$704$	−1.41167e9	−	8.15029e8i	−0.152486	−	0.0880377i
$705$	4.70687e9	+	3.84644e9i	0.505907	+	0.413426i
$706$			4.92169e8i			0.0526378i
$707$	5.40260e9	+	1.09941e10i	0.574956	+	1.17002i
$708$	1.43245e10	−	5.42544e9i	1.51692	−	0.574538i
$709$	−1.94150e9	−	3.36277e9i	−0.204585	−	0.354352i	0.745415	−	0.666601i	$-0.232251\pi$
$709$	−1.94150e9	−	3.36277e9i	−0.204585	−	0.354352i	−0.950001	+	0.312248i	$0.898918\pi$
$710$	−6.76252e9	+	1.17130e10i	−0.709095	+	1.22819i
$711$	−1.86307e9	−	9.16649e9i	−0.194395	−	0.956444i
$712$	−1.39567e10	+	8.05792e9i	−1.44912	+	0.836648i
$713$	−1.85380e10			−1.91535
$714$	7.70457e9	−	8.23738e9i	0.792145	−	0.846926i
$715$	−1.92615e9			−0.197070
$716$	−5.38532e9	+	3.10922e9i	−0.548297	+	0.316560i
$717$	7.36700e9	+	1.20053e9i	0.746404	+	0.121635i
$718$	1.01928e9	−	1.76544e9i	0.102768	−	0.177999i
$719$	−8.21012e9	−	1.42204e10i	−0.823756	−	1.42679i	−0.902866	−	0.429922i	$-0.858541\pi$
$719$	−8.21012e9	−	1.42204e10i	−0.823756	−	1.42679i	0.0791101	−	0.996866i	$-0.474792\pi$
$720$	−2.06518e10	+	1.82639e10i	−2.06203	+	1.82361i
$721$	1.62192e8	−	2.42265e9i	0.0161160	−	0.240722i
$722$			1.75552e9i			0.173591i
$723$	2.30722e9	−	2.82333e9i	0.227041	−	0.277829i
$724$	−1.74662e9	−	1.00841e9i	−0.171046	−	0.0987536i
$725$	2.53661e9	+	1.46451e9i	0.247213	+	0.142728i
$726$	−1.12130e10	+	1.37213e10i	−1.08754	+	1.33081i
$727$		−	4.75159e9i		−	0.458636i	−0.973351	−	0.229318i	$-0.926350\pi$
$727$		−	4.75159e9i		−	0.458636i	0.973351	−	0.229318i	$-0.0736497\pi$
$728$	−9.26269e9	+	1.38207e10i	−0.889769	+	1.32761i
$729$	−5.91974e9	−	8.62414e9i	−0.565921	−	0.824459i
$730$	6.72048e9	+	1.16402e10i	0.639396	+	1.10747i
$731$	−9.61291e8	+	1.66501e9i	−0.0910215	+	0.157654i
$732$	5.27109e9	+	8.58982e8i	0.496720	+	0.0809460i
$733$	−6.02688e9	+	3.47962e9i	−0.565235	+	0.326338i	−0.755244	−	0.655444i	$-0.772482\pi$
$733$	−6.02688e9	+	3.47962e9i	−0.565235	+	0.326338i	0.190009	+	0.981782i	$0.439148\pi$
$734$	3.52510e10			3.29030
$735$	−9.03185e9	−	9.65702e9i	−0.839017	−	0.897093i
$736$	3.02188e10			2.79386
$737$	2.40209e9	−	1.38685e9i	0.221031	−	0.127612i
$738$	1.88981e10	−	3.84100e9i	1.73070	−	0.351761i
$739$	2.73775e9	−	4.74193e9i	0.249539	−	0.432214i	−0.713859	−	0.700290i	$-0.753054\pi$
$739$	2.73775e9	−	4.74193e9i	0.249539	−	0.432214i	0.963398	+	0.268075i	$0.0863876\pi$
$740$	−2.08703e10	−	3.61485e10i	−1.89330	−	3.27928i
$741$	6.27144e9	−	2.37533e9i	0.566244	−	0.214467i
$742$	7.73853e9	−	1.15465e10i	0.695417	−	1.03762i
$743$		−	1.33440e10i		−	1.19351i	−0.802424	−	0.596755i	$-0.796457\pi$
$743$		−	1.33440e10i		−	1.19351i	0.802424	−	0.596755i	$-0.203543\pi$
$744$	−2.39864e10	−	1.96017e10i	−2.13531	−	1.74497i
$745$	4.05655e9	+	2.34205e9i	0.359427	+	0.207515i
$746$	−3.35927e8	−	1.93948e8i	−0.0296251	−	0.0171040i
$747$	7.52475e9	+	2.51939e9i	0.660496	+	0.221143i
$748$		−	4.31872e9i		−	0.377311i
$749$	−5.06627e8	+	7.56742e9i	−0.0440557	+	0.658054i
$750$	−4.53217e9	−	1.19660e10i	−0.392276	−	1.03570i
$751$	6.04666e9	+	1.04731e10i	0.520926	+	0.902270i	0.999704	+	0.0243339i	$0.00774648\pi$
$751$	6.04666e9	+	1.04731e10i	0.520926	+	0.902270i	−0.478778	+	0.877936i	$0.658920\pi$
$752$	6.95071e9	−	1.20390e10i	0.596028	−	1.03235i
$753$	−8.17324e7	+	5.01546e8i	−0.00697609	+	0.0428083i
$754$	6.68022e9	−	3.85683e9i	0.567533	−	0.327665i
$755$	1.79149e10			1.51496
$756$	−2.81268e10	−	7.84181e8i	−2.36752	−	0.0660070i
$757$	−5.16465e9			−0.432719			−0.216359	−	0.976314i	$-0.569418\pi$
$757$	−5.16465e9			−0.432719			−0.216359	+	0.976314i	$0.569418\pi$
$758$	1.85957e10	−	1.07362e10i	1.55085	−	0.895385i
$759$	−8.52159e8	+	5.22922e9i	−0.0707415	+	0.434101i
$760$	1.77619e10	−	3.07644e10i	1.46771	−	2.54215i
$761$	2.92989e9	+	5.07472e9i	0.240993	+	0.417413i	0.960998	−	0.276557i	$-0.0891935\pi$
$761$	2.92989e9	+	5.07472e9i	0.240993	+	0.417413i	−0.720004	+	0.693970i	$0.755860\pi$
$762$	−1.44758e10	−	3.82195e10i	−1.18522	−	3.12926i
$763$	8.07613e9	+	1.64347e10i	0.658214	+	1.33945i
$764$			4.18948e10i			3.39886i
$765$	−9.11295e9	−	3.05114e9i	−0.735942	−	0.246403i
$766$	−1.10859e10	−	6.40046e9i	−0.891192	−	0.514530i
$767$	−4.71641e9	−	2.72302e9i	−0.377422	−	0.217905i
$768$	−1.24951e10	−	1.02110e10i	−0.995348	−	0.813396i
$769$		−	1.46138e10i		−	1.15883i	−0.815033	−	0.579415i	$-0.803281\pi$
$769$		−	1.46138e10i		−	1.15883i	0.815033	−	0.579415i	$-0.196719\pi$
$770$	−7.18443e9	−	4.80987e8i	−0.567120	−	0.0379678i
$771$	−3.57235e9	+	1.35304e9i	−0.280714	+	0.106321i
$772$	2.07472e10	+	3.59352e10i	1.62293	+	2.81099i
$773$	−7.11062e9	+	1.23160e10i	−0.553706	+	0.959047i	0.444297	+	0.895880i	$0.353454\pi$
$773$	−7.11062e9	+	1.23160e10i	−0.553706	+	0.959047i	−0.998003	+	0.0631677i	$0.979880\pi$
$774$	6.68469e9	−	1.35865e9i	0.518189	−	0.105321i
$775$	−6.26848e9	+	3.61911e9i	−0.483734	+	0.279284i
$776$	1.25485e10			0.963998
$777$	3.85344e9	−	1.65778e10i	0.294696	−	1.26781i
$778$	−1.45826e10			−1.11021
$779$	−1.04624e10	+	6.04048e9i	−0.792959	+	0.457815i
$780$	2.42157e10	+	3.94621e9i	1.82711	+	0.297748i
$781$	−1.05582e9	+	1.82873e9i	−0.0793068	+	0.137363i
$782$	1.35262e10	+	2.34280e10i	1.01147	+	1.75191i
$783$	6.66950e9	+	3.51150e9i	0.496509	+	0.261413i
$784$	−1.84752e10	+	2.39384e10i	−1.36925	+	1.77415i
$785$			1.28707e10i			0.949636i
$786$	−1.30850e10	+	1.60121e10i	−0.961160	+	1.17617i
$787$	−1.24832e10	−	7.20717e9i	−0.912881	−	0.527052i	−0.0315238	−	0.999503i	$-0.510036\pi$
$787$	−1.24832e10	−	7.20717e9i	−0.912881	−	0.527052i	−0.881357	+	0.472451i	$0.843369\pi$
$788$	−2.60067e9	−	1.50150e9i	−0.189340	−	0.109316i
$789$	−7.48896e9	+	9.16419e9i	−0.542815	+	0.664239i
$790$			3.04905e10i			2.20024i
$791$	−8.11973e9	−	5.44187e9i	−0.583343	−	0.390959i
$792$	−6.63189e9	+	5.86508e9i	−0.474350	+	0.419504i
$793$	−9.49412e8	−	1.64443e9i	−0.0676081	−	0.117101i
$794$	6.12406e9	−	1.06072e10i	0.434178	−	0.752018i
$795$	−1.16891e10	−	1.90487e9i	−0.825082	−	0.134456i
$796$	6.18482e9	−	3.57081e9i	0.434642	−	0.250941i
$797$	−8.69993e9			−0.608712			−0.304356	−	0.952558i	$-0.598441\pi$
$797$	−8.69993e9			−0.608712			−0.304356	+	0.952558i	$0.598441\pi$
$798$	2.39852e10	−	7.29378e9i	1.67084	−	0.508092i
$799$	4.84578e9			0.336085
$800$	1.02183e10	−	5.89952e9i	0.705606	−	0.407382i
$801$	1.93011e9	+	9.49632e9i	0.132699	+	0.652892i
$802$	2.25577e9	−	3.90710e9i	0.154413	−	0.267451i
$803$	1.04925e9	+	1.81736e9i	0.0715116	+	0.123862i
$804$	−3.30405e10	+	1.25142e10i	−2.24208	+	0.849196i
$805$	2.84627e10	−	1.39868e10i	1.92305	−	0.945002i
$806$			1.90620e10i			1.28232i
$807$	2.03272e10	+	1.66114e10i	1.36151	+	1.11262i
$808$	−4.25182e10	−	2.45479e10i	−2.83554	−	1.63710i
$809$	−6.69790e9	−	3.86704e9i	−0.444753	−	0.256778i	0.260859	−	0.965377i	$-0.415994\pi$
$809$	−6.69790e9	−	3.86704e9i	−0.444753	−	0.256778i	−0.705612	+	0.708599i	$0.749328\pi$
$810$	1.33105e10	+	3.13918e10i	0.880027	+	2.07548i
$811$			2.54241e9i			0.167368i	0.996492	+	0.0836841i	$0.0266687\pi$
$811$			2.54241e9i			0.167368i	−0.996492	+	0.0836841i	$0.973331\pi$
$812$	1.81969e10	−	8.94207e9i	1.19275	−	0.586127i
$813$	7.73114e9	+	2.04120e10i	0.504576	+	1.33220i
$814$	−4.63422e9	−	8.02670e9i	−0.301156	−	0.521617i
$815$	1.62076e10	−	2.80724e10i	1.04874	−	1.81647i
$816$	−3.53489e9	+	2.16916e10i	−0.227751	+	1.39758i
$817$	−3.70080e9	+	2.13666e9i	−0.237421	+	0.137075i
$818$	−3.83604e10			−2.45045
$819$	6.11212e9	+	7.91998e9i	0.388775	+	0.503768i
$820$	−4.41990e10			−2.79939
$821$	2.37082e10	−	1.36879e10i	1.49519	−	0.863250i	0.495208	−	0.868774i	$-0.335092\pi$
$821$	2.37082e10	−	1.36879e10i	1.49519	−	0.863250i	0.999985	+	0.00552400i	$0.00175835\pi$
$822$	−3.02402e9	+	1.85567e10i	−0.189904	+	1.16533i
$823$	−5.06880e9	+	8.77942e9i	−0.316961	+	0.548992i	−0.979852	−	0.199723i	$-0.935996\pi$
$823$	−5.06880e9	+	8.77942e9i	−0.316961	+	0.548992i	0.662892	+	0.748715i	$0.269329\pi$
$824$	4.86569e9	+	8.42762e9i	0.302970	+	0.524759i
$825$	7.32733e8	+	1.93459e9i	0.0454315	+	0.119950i
$826$	−1.69119e10	−	1.13344e10i	−1.04415	−	0.699793i
$827$		−	1.43439e10i		−	0.881858i	−0.897542	−	0.440929i	$-0.854649\pi$
$827$		−	1.43439e10i		−	0.881858i	0.897542	−	0.440929i	$-0.145351\pi$
$828$	2.14267e10	−	6.39961e10i	1.31175	−	3.91784i
$829$	1.51191e10	+	8.72901e9i	0.921690	+	0.532138i	0.884174	−	0.467158i	$-0.154722\pi$
$829$	1.51191e10	+	8.72901e9i	0.921690	+	0.532138i	0.0375162	+	0.999296i	$0.488055\pi$
$830$	−2.24009e10	−	1.29332e10i	−1.35985	−	0.785112i
$831$	4.64489e9	+	3.79580e9i	0.280784	+	0.229456i
$832$		−	7.38232e9i		−	0.444387i
$833$	−1.04466e10	−	1.40507e9i	−0.626206	−	0.0842246i
$834$	3.81789e10	−	1.44604e10i	2.27899	−	0.863175i
$835$	−4.70357e9	−	8.14681e9i	−0.279592	−	0.484267i
$836$	4.79961e9	−	8.31316e9i	0.284108	−	0.492090i
$837$	−1.57559e10	+	9.93474e9i	−0.928760	+	0.585622i
$838$	4.30224e10	−	2.48390e10i	2.52546	−	1.45808i
$839$	2.21478e10			1.29468			0.647341	−	0.762200i	$-0.275881\pi$
$839$	2.21478e10			1.29468			0.647341	+	0.762200i	$0.275881\pi$
$840$	5.16175e10	+	1.19983e10i	3.00483	+	0.698459i
$841$	1.18186e10			0.685142
$842$	−5.19436e10	+	2.99896e10i	−2.99874	+	1.73133i
$843$	−1.56168e9	−	2.54492e8i	−0.0897831	−	0.0146312i
$844$	−1.31576e9	+	2.27897e9i	−0.0753320	+	0.130479i
$845$	6.40978e9	+	1.11021e10i	0.365464	+	0.633002i
$846$	−1.13899e10	−	1.28790e10i	−0.646728	−	0.731282i
$847$	1.65233e10	+	1.10621e9i	0.934338	+	0.0625525i
$848$			2.70849e10i			1.52525i
$849$	−7.87700e9	+	9.63904e9i	−0.441757	+	0.540576i
$850$	9.14756e9	+	5.28135e9i	0.510904	+	0.294970i
$851$	3.53525e10	+	2.04108e10i	1.96638	+	1.13529i
$852$	1.70204e10	−	2.08278e10i	0.942825	−	1.15373i
$853$		−	2.54298e10i		−	1.40288i	−0.712727	−	0.701442i	$-0.752540\pi$
$853$		−	2.54298e10i		−	1.40288i	0.712727	−	0.701442i	$-0.247460\pi$
$854$	−3.13061e9	−	6.37070e9i	−0.171999	−	0.350013i
$855$	−1.41507e10	−	1.60008e10i	−0.774279	−	0.875510i
$856$	−1.51986e10	−	2.63247e10i	−0.828217	−	1.43451i
$857$	−5.19220e9	+	8.99316e9i	−0.281786	+	0.488067i	−0.971825	−	0.235705i	$-0.924260\pi$
$857$	−5.19220e9	+	8.99316e9i	−0.281786	+	0.488067i	0.690039	+	0.723772i	$0.257593\pi$
$858$	5.37705e9	+	8.76249e8i	0.290629	+	0.0473611i
$859$	1.70758e9	−	9.85872e8i	0.0919189	−	0.0530694i	−0.453336	−	0.891340i	$-0.649766\pi$
$859$	1.70758e9	−	9.85872e8i	0.0919189	−	0.0530694i	0.545255	+	0.838270i	$0.316433\pi$
$860$	−1.56342e10			−0.838169
$861$	−1.31622e10	−	1.23108e10i	−0.702775	−	0.657318i
$862$	−5.78939e10			−3.07863
$863$	−1.48990e10	+	8.60195e9i	−0.789078	+	0.455574i	−0.839638	−	0.543147i	$-0.817233\pi$
$863$	−1.48990e10	+	8.60195e9i	−0.789078	+	0.455574i	0.0505599	+	0.998721i	$0.483899\pi$
$864$	2.56837e10	−	1.61947e10i	1.35475	−	0.854228i
$865$	−1.08646e10	+	1.88181e10i	−0.570767	+	0.988597i
$866$	−2.25823e10	−	3.91136e10i	−1.18156	−	2.04652i
$867$	1.07812e10	−	4.08342e9i	0.561824	−	0.212793i
$868$	−3.34691e9	+	4.99923e10i	−0.173710	+	2.59468i
$869$			4.76042e9i			0.246080i
$870$	−1.90248e10	−	1.55470e10i	−0.979497	−	0.800443i
$871$	1.08788e10	+	6.28086e9i	0.557849	+	0.322074i
$872$	−6.35588e10	−	3.66957e10i	−3.24614	−	1.87416i
$873$	2.39561e9	−	7.15505e9i	0.121861	−	0.363968i
$874$			6.01292e10i			3.04646i
$875$	−6.65740e9	+	9.93340e9i	−0.335951	+	0.501267i
$876$	−9.46794e9	−	2.49976e10i	−0.475873	−	1.25642i
$877$	−1.06426e10	−	1.84336e10i	−0.532783	−	0.922806i	−0.999267	−	0.0382771i	$-0.987813\pi$
$877$	−1.06426e10	−	1.84336e10i	−0.532783	−	0.922806i	0.466485	−	0.884529i	$-0.345520\pi$
$878$	3.45775e10	−	5.98900e10i	1.72410	−	2.98623i
$879$	2.91824e9	−	1.79076e10i	0.144930	−	0.889357i
$880$	1.21509e10	−	7.01533e9i	0.601062	−	0.347023i
$881$	1.34320e10			0.661798			0.330899	−	0.943666i	$-0.392648\pi$
$881$	1.34320e10			0.661798			0.330899	+	0.943666i	$0.392648\pi$
$882$	2.08201e10	+	3.10673e10i	1.02174	+	1.52462i
$883$	2.56922e9			0.125585			0.0627927	−	0.998027i	$-0.479999\pi$
$883$	2.56922e9			0.125585			0.0627927	+	0.998027i	$0.479999\pi$
$884$	1.69385e10	−	9.77947e9i	0.824695	−	0.476138i
$885$	−2.79002e9	+	1.71208e10i	−0.135302	+	0.830274i
$886$	5.91404e9	−	1.02434e10i	0.285671	−	0.494797i
$887$	−1.68588e9	−	2.92004e9i	−0.0811138	−	0.140493i	0.822615	−	0.568599i	$-0.192514\pi$
$887$	−1.68588e9	−	2.92004e9i	−0.0811138	−	0.140493i	−0.903729	+	0.428106i	$0.859181\pi$
$888$	2.41610e10	+	6.37908e10i	1.15790	+	3.05712i
$889$	−2.12638e10	+	3.17273e10i	−1.01504	+	1.51453i
$890$		−	3.15876e10i		−	1.50193i
$891$	2.07814e9	+	4.90113e9i	0.0984244	+	0.232126i
$892$	5.00580e10	+	2.89010e10i	2.36155	+	1.36344i
$893$	9.32769e9	+	5.38534e9i	0.438323	+	0.253066i
$894$	−1.02588e10	−	8.38347e9i	−0.480193	−	0.392412i
$895$		−	7.04220e9i		−	0.328343i
$896$	−4.60077e8	+	6.87211e9i	−0.0213675	+	0.319163i
$897$	−2.24393e10	+	8.49897e9i	−1.03809	+	0.393181i
$898$	3.98254e8	+	6.89796e8i	0.0183524	+	0.0317873i
$899$	6.71087e9	−	1.16236e10i	0.308049	−	0.533556i
$900$	−5.24845e9	−	2.58229e10i	−0.239984	−	1.18075i
$901$	−8.17639e9	+	4.72064e9i	−0.372413	+	0.215013i
$902$	−9.81431e9			−0.445284
$903$	−4.65576e9	−	4.35462e9i	−0.210418	−	0.196808i
$904$	3.91755e10			1.76370
$905$	1.97800e9	−	1.14200e9i	0.0887065	−	0.0512147i
$906$	−5.00113e10	−	8.14988e9i	−2.23418	−	0.364085i
$907$	1.80966e9	−	3.13443e9i	0.0805327	−	0.139487i	−0.822946	−	0.568119i	$-0.807671\pi$
$907$	1.80966e9	−	3.13443e9i	0.0805327	−	0.139487i	0.903479	+	0.428633i	$0.141005\pi$
$908$	4.64682e10	+	8.04854e10i	2.05995	+	3.56793i
$909$	−2.21140e10	+	1.95571e10i	−0.976550	+	0.863637i
$910$	−1.43822e10	−	2.92673e10i	−0.632674	−	1.28747i
$911$		−	3.28292e10i		−	1.43862i	−0.694688	−	0.719311i	$-0.744458\pi$
$911$		−	3.28292e10i		−	1.43862i	0.694688	−	0.719311i	$-0.255542\pi$
$912$	−3.09113e10	+	3.78260e10i	−1.34938	+	1.65123i
$913$	−3.49741e9	−	2.01923e9i	−0.152089	−	0.0878088i
$914$	6.03437e9	+	3.48395e9i	0.261409	+	0.150925i
$915$	−3.82712e9	+	4.68323e9i	−0.165158	+	0.202102i
$916$		−	8.63661e10i		−	3.71286i
$917$	1.92819e10	+	1.29089e9i	0.825765	+	0.0552837i
$918$	2.40516e10	+	1.26632e10i	1.02611	+	0.540250i
$919$	−6.37342e9	−	1.10391e10i	−0.270875	−	0.469169i	0.698211	−	0.715892i	$-0.253980\pi$
$919$	−6.37342e9	−	1.10391e10i	−0.270875	−	0.469169i	−0.969086	+	0.246723i	$0.920646\pi$
$920$	−6.35521e10	+	1.10076e11i	−2.69075	+	4.66051i
$921$	−1.13280e10	−	1.84602e9i	−0.477799	−	0.0778625i
$922$	−3.44157e10	+	1.98699e10i	−1.44610	+	0.834906i
$923$	−9.56333e9			−0.400316
$924$	1.39481e10	+	3.24217e9i	0.581651	+	0.135202i
$925$	1.59389e10			0.662161
$926$	4.26637e10	−	2.46319e10i	1.76571	−	1.01944i
$927$	5.73425e9	−	1.16548e9i	0.236427	−	0.0480534i
$928$	−1.09394e10	+	1.89476e10i	−0.449341	+	0.778281i
$929$	−1.06936e10	−	1.85219e10i	−0.437593	−	0.757933i	0.559911	−	0.828553i	$-0.310835\pi$
$929$	−1.06936e10	−	1.85219e10i	−0.437593	−	0.757933i	−0.997503	+	0.0706204i	$0.977502\pi$
$930$	5.67797e10	−	2.15055e10i	2.31474	−	0.876718i
$931$	−1.85473e10	−	1.43144e10i	−0.753279	−	0.581367i
$932$		−	1.28821e8i		−	0.00521233i
$933$	−1.83387e10	−	1.49864e10i	−0.739237	−	0.604102i
$934$	−3.03491e10	−	1.75221e10i	−1.21880	−	0.703674i
$935$	4.23558e9	+	2.44541e9i	0.169462	+	0.0978390i
$936$	−3.80210e10	−	1.27299e10i	−1.51551	−	0.507413i
$937$		−	1.55091e10i		−	0.615884i	−0.951405	−	0.307942i	$-0.900360\pi$
$937$		−	1.55091e10i		−	0.615884i	0.951405	−	0.307942i	$-0.0996402\pi$
$938$	3.90087e10	+	2.61438e10i	1.54330	+	1.03433i
$939$	5.43867e9	+	1.43594e10i	0.214370	+	0.565986i
$940$	1.97026e10	+	3.41260e10i	0.773708	+	1.34010i
$941$	4.75703e9	−	8.23941e9i	0.186111	−	0.322354i	−0.757839	−	0.652441i	$-0.773745\pi$
$941$	4.75703e9	−	8.23941e9i	0.186111	−	0.322354i	0.943950	+	0.330088i	$0.107078\pi$
$942$	5.85514e9	−	3.59297e10i	0.228223	−	1.40047i
$943$	3.74346e10	−	2.16129e10i	1.45373	−	0.839309i
$944$	3.96705e10			1.53485
$945$	1.66955e10	−	2.71413e10i	0.643558	−	1.04621i
$946$	−3.47155e9			−0.133323
$947$	9.90388e8	−	5.71801e8i	0.0378949	−	0.0218786i	−0.480933	−	0.876757i	$-0.659702\pi$
$947$	9.90388e8	−	5.71801e8i	0.0378949	−	0.0218786i	0.518828	+	0.854879i	$0.326369\pi$
$948$	9.75290e9	−	5.98481e10i	0.371796	−	2.28150i
$949$	−4.75194e9	+	8.23060e9i	−0.180484	+	0.312608i
$950$	1.17388e10	+	2.03322e10i	0.444214	+	0.769401i
$951$	1.19719e10	+	3.16088e10i	0.451370	+	1.19172i
$952$	3.79150e10	−	1.86317e10i	1.42424	−	0.699880i
$953$			2.71794e10i			1.01722i	0.860997	+	0.508611i	$0.169841\pi$
$953$			2.71794e10i			1.01722i	−0.860997	+	0.508611i	$0.830159\pi$
$954$	3.17648e10	+	1.06353e10i	1.18448	+	0.396578i
$955$	−4.10883e10	−	2.37223e10i	−1.52653	−	0.881344i
$956$	4.19046e10	+	2.41936e10i	1.55117	+	0.895567i
$957$	−2.97031e9	−	2.42733e9i	−0.109549	−	0.0895235i
$958$			5.30430e10i			1.94917i
$959$	1.57696e10	−	7.74931e9i	0.577373	−	0.283725i
$960$	−2.19896e10	+	8.32865e9i	−0.802173	+	0.303826i
$961$	2.82760e9	+	4.89755e9i	0.102775	+	0.178011i
$962$	2.09878e10	−	3.63519e10i	0.760070	−	1.31648i
$963$	−1.79116e10	+	3.64050e9i	−0.646313	+	0.131362i
$964$	2.04699e10	−	1.18183e10i	0.735945	−	0.424898i
$965$	−4.69912e10			−1.68334
$966$	−8.58194e10	+	2.60972e10i	−3.06313	+	0.931481i
$967$	3.61731e10			1.28645			0.643226	−	0.765676i	$-0.277596\pi$
$967$	3.61731e10			1.28645			0.643226	+	0.765676i	$0.277596\pi$
$968$	−5.74793e10	+	3.31857e10i	−2.03680	+	1.17594i
$969$	−1.68065e10	−	2.73880e9i	−0.593395	−	0.0967002i
$970$	−1.22977e10	+	2.13003e10i	−0.432638	+	0.749350i
$971$	−2.21056e10	−	3.82880e10i	−0.774880	−	1.34213i	−0.934862	−	0.355011i	$-0.884477\pi$
$971$	−2.21056e10	−	3.82880e10i	−0.774880	−	1.34213i	0.159982	−	0.987120i	$-0.448856\pi$
$972$	−1.60852e10	−	6.58748e10i	−0.561818	−	2.30084i
$973$	−3.16936e10	−	2.12412e10i	−1.10300	−	0.739237i
$974$			5.77720e10i			2.00337i
$975$	−5.92846e9	+	7.25462e9i	−0.204845	+	0.250668i
$976$	1.19785e10	+	6.91579e9i	0.412409	+	0.238104i
$977$	1.60822e10	+	9.28504e9i	0.551714	+	0.318532i	0.749813	−	0.661650i	$-0.230144\pi$
$977$	1.60822e10	+	9.28504e9i	0.551714	+	0.318532i	−0.198099	+	0.980182i	$0.563477\pi$
$978$	−5.80159e10	+	7.09937e10i	−1.98317	+	2.42680i
$979$		−	4.93170e9i		−	0.167980i
$980$	−3.25802e10	−	7.92823e10i	−1.10576	−	2.69082i
$981$	−3.30574e10	+	2.92352e10i	−1.11796	+	0.988699i
$982$	4.57764e10	+	7.92870e10i	1.54259	+	2.67185i
$983$	−2.26864e10	+	3.92940e10i	−0.761778	+	1.31944i	0.180155	+	0.983638i	$0.442340\pi$
$983$	−2.26864e10	+	3.92940e10i	−0.761778	+	1.31944i	−0.941933	+	0.335800i	$0.890993\pi$
$984$	7.12900e10	+	1.16175e10i	2.38532	+	0.388714i
$985$	2.94518e9	−	1.70040e9i	0.0981941	−	0.0566924i
$986$	−1.95863e10			−0.650703
$987$	−3.63784e9	+	1.56503e10i	−0.120430	+	0.518098i
$988$	4.34736e10			1.43409
$989$	1.32415e10	−	7.64499e9i	0.435261	−	0.251298i
$990$	−3.45625e9	−	1.70051e10i	−0.113209	−	0.557001i
$991$	9.67372e9	−	1.67554e10i	0.315744	−	0.546885i	−0.663851	−	0.747865i	$-0.731079\pi$
$991$	9.67372e9	−	1.67554e10i	0.315744	−	0.546885i	0.979595	+	0.200980i	$0.0644125\pi$
$992$	−2.70335e10	−	4.68233e10i	−0.879247	−	1.52290i
$993$	1.91857e10	−	7.26667e9i	0.621808	−	0.235512i
$994$	−3.56706e10	−	2.38809e9i	−1.15201	−	0.0771256i
$995$			8.08768e9i			0.260281i
$996$	3.98326e10	+	3.25511e10i	1.27741	+	1.04390i
$997$	4.94707e10	+	2.85619e10i	1.58094	+	0.912755i	0.994723	+	0.102600i	$0.0327161\pi$
$997$	4.94707e10	+	2.85619e10i	1.58094	+	0.912755i	0.586215	+	0.810155i	$0.300617\pi$
$998$	−1.57642e10	−	9.10148e9i	−0.502014	−	0.289838i
$999$	4.09854e10	−	1.59825e9i	1.30062	−	0.0507183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.g.b.17.16	yes	32
3.2	odd	2	inner	21.8.g.b.17.1	yes	32
7.3	odd	6		147.8.c.b.146.6		32
7.4	even	3		147.8.c.b.146.28		32
7.5	odd	6	inner	21.8.g.b.5.1	✓	32
21.5	even	6	inner	21.8.g.b.5.16	yes	32
21.11	odd	6		147.8.c.b.146.5		32
21.17	even	6		147.8.c.b.146.27		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.1	✓	32	7.5	odd	6	inner
21.8.g.b.5.16	yes	32	21.5	even	6	inner
21.8.g.b.17.1	yes	32	3.2	odd	2	inner
21.8.g.b.17.16	yes	32	1.1	even	1	trivial
147.8.c.b.146.5		32	21.11	odd	6
147.8.c.b.146.6		32	7.3	odd	6
147.8.c.b.146.27		32	21.17	even	6
147.8.c.b.146.28		32	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.9825 - 10.3822i) q^{2} +(7.52171 - 46.1565i) q^{3} +(151.580 - 262.545i) q^{4} +(171.660 + 297.324i) q^{5} +(-343.947 - 908.102i) q^{6} +(-505.231 + 753.847i) q^{7} -3637.11i q^{8} +(-2073.85 - 694.352i) q^{9} +(6173.77 + 3564.43i) q^{10} +(963.898 + 556.507i) q^{11} +(-10978.0 - 8971.21i) q^{12} +5040.70i q^{13} +(-1258.73 + 18801.5i) q^{14} +(15014.6 - 5686.86i) q^{15} +(-18358.9 - 31798.6i) q^{16} +(6399.59 - 11084.4i) q^{17} +(-44501.9 + 9044.92i) q^{18} +(24637.3 - 14224.3i) q^{19} +104081. q^{20} +(30994.7 + 28989.9i) q^{21} +23111.1 q^{22} +(-88152.4 + 50894.8i) q^{23} +(-167876. - 27357.3i) q^{24} +(-19872.1 + 34419.4i) q^{25} +(52333.5 + 90644.4i) q^{26} +(-47647.8 + 90498.9i) q^{27} +(121335. + 246914. i) q^{28} -73697.1i q^{29} +(210959. - 258149. i) q^{30} +(157721. + 91060.2i) q^{31} +(-257101. - 148437. i) q^{32} +(32936.6 - 40304.3i) q^{33} -265767. i q^{34} +(-310865. - 20812.0i) q^{35} +(-496653. + 439228. i) q^{36} +(-200519. - 347310. i) q^{37} +(295360. - 511578. i) q^{38} +(232661. + 37914.7i) q^{39} +(1.08140e6 - 624348. i) q^{40} -424658. q^{41} +(858342. + 199518. i) q^{42} -150211. q^{43} +(292216. - 168711. i) q^{44} +(-149550. - 735798. i) q^{45} +(-1.05680e6 + 1.83043e6i) q^{46} +(189300. + 327878. i) q^{47} +(-1.60580e6 + 608204. i) q^{48} +(-313026. - 761733. i) q^{49} +825264. i q^{50} +(-463482. - 378756. i) q^{51} +(1.32341e6 + 764071. i) q^{52} +(-638822. - 368824. i) q^{53} +(82751.8 + 2.12209e6i) q^{54} +382121. i q^{55} +(2.74182e6 + 1.83758e6i) q^{56} +(-471231. - 1.24416e6i) q^{57} +(-765138. - 1.32526e6i) q^{58} +(-540207. + 935666. i) q^{59} +(782870. - 4.80403e6i) q^{60} +(-326231. + 188349. i) q^{61} +3.78162e6 q^{62} +(1.57121e6 - 1.21255e6i) q^{63} -1.46454e6 q^{64} +(-1.49872e6 + 865288. i) q^{65} +(173835. - 1.06673e6i) q^{66} +(1.24603e6 - 2.15819e6i) q^{67} +(-1.94010e6 - 3.36036e6i) q^{68} +(1.68607e6 + 4.45162e6i) q^{69} +(-5.80621e6 + 2.85322e6i) q^{70} +1.89722e6i q^{71} +(-2.52543e6 + 7.54281e6i) q^{72} +(1.63283e6 + 942715. i) q^{73} +(-7.21168e6 - 4.16367e6i) q^{74} +(1.43921e6 + 1.17612e6i) q^{75} -8.62452e6i q^{76} +(-906512. + 445467. i) q^{77} +(4.57747e6 - 1.73373e6i) q^{78} +(2.13852e6 + 3.70403e6i) q^{79} +(6.30300e6 - 1.09171e7i) q^{80} +(3.81872e6 + 2.87996e6i) q^{81} +(-7.63642e6 + 4.40889e6i) q^{82} -3.62840e6 q^{83} +(1.23093e7 - 3.74321e6i) q^{84} +4.39422e6 q^{85} +(-2.70118e6 + 1.55953e6i) q^{86} +(-3.40160e6 - 554328. i) q^{87} +(2.02408e6 - 3.50580e6i) q^{88} +(-2.21547e6 - 3.83731e6i) q^{89} +(-1.03285e7 - 1.16788e7i) q^{90} +(-3.79991e6 - 2.54672e6i) q^{91} +3.08586e7i q^{92} +(5.38935e6 - 6.59492e6i) q^{93} +(6.80819e6 + 3.93071e6i) q^{94} +(8.45849e6 + 4.88351e6i) q^{95} +(-8.78520e6 + 1.07504e7i) q^{96} +3.45013e6i q^{97} +(-1.35375e7 - 1.04480e7i) q^{98} +(-1.61257e6 - 1.82340e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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